10010010@unknown@formal@none@1@S@<article>Algorithm</article>@@@@1@1@@oe@19-8-2009
10010020@unknown@formal@none@1@S@In [[mathematics]], [[computing]], [[linguistics]] and related disciplines, an '''algorithm''' is a sequence of instructions, often used for [[calculation]] and [[data processing]].@@@@1@21@@oe@19-8-2009
10010030@unknown@formal@none@1@S@It is formally a type of [[effective method]] in which a list of well-defined instructions for completing a task will, when given an initial state, proceed through a well-defined series of successive states, eventually terminating in an end-state.@@@@1@38@@oe@19-8-2009
10010040@unknown@formal@none@1@S@The transition from one state to the next is not necessarily [[deterministic]]; some algorithms, known as [[probabilistic algorithms]], incorporate randomness.@@@@1@20@@oe@19-8-2009
10010050@unknown@formal@none@1@S@A partial formalization of the concept began with attempts to solve the [[Entscheidungsproblem]] (the "decision problem") posed by [[David Hilbert]] in 1928.@@@@1@22@@oe@19-8-2009
10010060@unknown@formal@none@1@S@Subsequent formalizations were framed as attempts to define "[[effective calculability]]" (Kleene 1943:274) or "effective method" (Rosser 1939:225); those formalizations included the Gödel-Herbrand-Kleene [[Recursion (computer science)|recursive function]]s of 1930, 1934 and 1935, [[Alonzo Church]]'s [[lambda calculus]] of 1936, [[Emil Post]]'s "Formulation I" of 1936, and [[Alan Turing]]'s [[Turing machines]] of 1936-7 and 1939.@@@@1@52@@oe@19-8-2009
10010070@unknown@formal@none@1@S@==Etymology==@@@@1@1@@oe@19-8-2009
10010080@unknown@formal@none@1@S@[[Muhammad ibn Mūsā al-Khwārizmī|Al-Khwārizmī]], [[Persian people|Persian]] [[astronomer]] and [[mathematician]], wrote a [[treatise]] in [[Arabic]] in 825 AD, ''On Calculation with Hindu Numerals''.@@@@1@22@@oe@19-8-2009
10010090@unknown@formal@none@1@S@(See [[algorism]]).@@@@1@2@@oe@19-8-2009
10010100@unknown@formal@none@1@S@It was translated into [[Latin]] in the 12th century as ''Algoritmi de numero Indorum'' (al-Daffa 1977), which title was likely intended to mean "Algoritmi on the numbers of the Indians", where "Algoritmi" was the translator's rendition of the author's name; but people misunderstanding the title treated ''Algoritmi'' as a Latin plural and this led to the word "algorithm" (Latin ''algorismus'') coming to mean "calculation method".@@@@1@65@@oe@19-8-2009
10010110@unknown@formal@none@1@S@The intrusive "th" is most likely due to a [[false cognate]] with the [[Greek language|Greek]] {{lang|grc|ἀριθμός}} (''arithmos'') meaning "number".@@@@1@19@@oe@19-8-2009
10010120@unknown@formal@none@1@S@== Why algorithms are necessary: an informal definition ==@@@@1@9@@oe@19-8-2009
10010130@unknown@formal@none@1@S@No generally accepted ''formal'' definition of "algorithm" exists yet.@@@@1@9@@oe@19-8-2009
10010140@unknown@formal@none@1@S@An informal definition could be "an algorithm is a computer program that calculates something."@@@@1@14@@oe@19-8-2009
10010150@unknown@formal@none@1@S@For some people, a program is only an algorithm if it stops eventually.@@@@1@13@@oe@19-8-2009
10010160@unknown@formal@none@1@S@For others, a program is only an algorithm if it stops before a given number of calculation steps.@@@@1@18@@oe@19-8-2009
10010170@unknown@formal@none@1@S@A prototypical example of an "algorithm" is Euclid's algorithm to determine the maximum common divisor of two integers greater than one: "subtract the smallest number from the biggest one, repeat until you get a zero or a one".@@@@1@38@@oe@19-8-2009
10010180@unknown@formal@none@1@S@This procedure is know to stop always, and the number of subtractions needed is always smaller than the biggest of the two numbers.@@@@1@23@@oe@19-8-2009
10010190@unknown@formal@none@1@S@We can derive clues to the issues involved and an informal meaning of the word from the following quotation from {{Harvtxt|Boolos|Jeffrey|1974, 1999}} (boldface added):@@@@1@24@@oe@19-8-2009
10010200@unknown@formal@none@1@S@<blockquote> No human being can write fast enough, or long enough, or small enough to list all members of an enumerably infinite set by writing out their names, one after another, in some notation.@@@@1@34@@oe@19-8-2009
10010210@unknown@formal@none@1@S@But humans can do something equally useful, in the case of certain enumerably infinite sets: They can give '''explicit instructions for determining the nth member of the set''', for arbitrary finite n.@@@@1@32@@oe@19-8-2009
10010220@unknown@formal@none@1@S@Such instructions are to be given quite explicitly, in a form in which '''they could be followed by a computing machine''', or by a '''human who is capable of carrying out only very elementary operations on symbols''' </blockquote>@@@@1@38@@oe@19-8-2009
10010230@unknown@formal@none@1@S@The words "enumerably infinite" mean "countable using integers perhaps extending to infinity".@@@@1@12@@oe@19-8-2009
10010240@unknown@formal@none@1@S@Thus Boolos and Jeffrey are saying that an algorithm ''implies'' instructions for a process that "creates" output integers from an ''arbitrary'' "input" integer or integers that, in theory, can be chosen from 0 to infinity.@@@@1@35@@oe@19-8-2009
10010250@unknown@formal@none@1@S@Thus we might expect an algorithm to be an algebraic equation such as '''y = m + n''' — two arbitrary "input variables" '''m''' and '''n''' that produce an output '''y'''.@@@@1@31@@oe@19-8-2009
10010260@unknown@formal@none@1@S@As we see in [[Algorithm characterizations]] — the word algorithm implies much more than this, something on the order of (for our addition example):@@@@1@24@@oe@19-8-2009
10010270@unknown@formal@none@1@S@:Precise instructions (in language understood by "the computer") for a "fast, efficient, good" ''process'' that specifies the "moves" of "the computer" (machine or human, equipped with the necessary internally-contained information and capabilities) to find, decode, and then munch arbitrary input integers/symbols '''m''' and '''n''', symbols '''+''' and '''=''' ... and (reliably, correctly, "effectively") produce, in a "reasonable" [[time]], output-integer '''y''' at a specified place and in a specified format.@@@@1@69@@oe@19-8-2009
10010280@unknown@formal@none@1@S@The concept of ''algorithm'' is also used to define the notion of [[decidability (logic)|decidability]].@@@@1@14@@oe@19-8-2009
10010290@unknown@formal@none@1@S@That notion is central for explaining how [[formal system]]s come into being starting from a small set of [[axiom]]s and rules.@@@@1@21@@oe@19-8-2009
10010300@unknown@formal@none@1@S@In [[logic]], the time that an algorithm requires to complete cannot be measured, as it is not apparently related with our customary physical dimension.@@@@1@24@@oe@19-8-2009
10010310@unknown@formal@none@1@S@From such uncertainties, that characterize ongoing work, stems the unavailability of a definition of ''algorithm'' that suits both concrete (in some sense) and abstract usage of the term.@@@@1@28@@oe@19-8-2009
10010320@unknown@formal@none@1@S@:''For a detailed presentation of the various points of view around the definition of "algorithm" see [[Algorithm characterizations]].@@@@1@18@@oe@19-8-2009
10010330@unknown@formal@none@1@S@For examples of simple addition algorithms specified in the detailed manner described in [[Algorithm characterizations]], see [[Algorithm examples]].''@@@@1@18@@oe@19-8-2009
10010340@unknown@formal@none@1@S@== Formalization of algorithms ==@@@@1@5@@oe@19-8-2009
10010350@unknown@formal@none@1@S@Algorithms are essential to the way [[computer]]s process information, because a [[computer program]] is essentially an algorithm that tells the computer what specific steps to perform (in what specific order) in order to carry out a specified task, such as calculating employees’ paychecks or printing students’ report cards.@@@@1@48@@oe@19-8-2009
10010360@unknown@formal@none@1@S@Thus, an algorithm can be considered to be any sequence of operations that can be performed by a [[Turing completeness|Turing-complete]] system.@@@@1@21@@oe@19-8-2009
10010370@unknown@formal@none@1@S@Authors who assert this thesis include Savage (1987) and Gurevich (2000):@@@@1@11@@oe@19-8-2009
10010380@unknown@formal@none@1@S@<blockquote> ...Turing's informal argument in favor of his thesis justifies a stronger thesis: every algorithm can be simulated by a Turing machine (Gurevich 2000:1)...according to Savage [1987], an algorithm is a computational process defined by a Turing machine.@@@@1@38@@oe@19-8-2009
10010390@unknown@formal@none@1@S@(Gurevich 2000:3) </blockquote>@@@@1@3@@oe@19-8-2009
10010400@unknown@formal@none@1@S@Typically, when an algorithm is associated with processing information, data are read from an input source or device, written to an output sink or device, and/or stored for further processing.@@@@1@30@@oe@19-8-2009
10010410@unknown@formal@none@1@S@Stored data are regarded as part of the internal state of the entity performing the algorithm.@@@@1@16@@oe@19-8-2009
10010420@unknown@formal@none@1@S@In practice, the state is stored in a [[data structure]], but an algorithm requires the internal data only for specific operation sets called [[abstract data type]]s.@@@@1@26@@oe@19-8-2009
10010430@unknown@formal@none@1@S@For any such computational process, the algorithm must be rigorously defined: specified in the way it applies in all possible circumstances that could arise.@@@@1@24@@oe@19-8-2009
10010440@unknown@formal@none@1@S@That is, any conditional steps must be systematically dealt with, case-by-case; the criteria for each case must be clear (and computable).@@@@1@21@@oe@19-8-2009
10010450@unknown@formal@none@1@S@Because an algorithm is a precise list of precise steps, the order of computation will almost always be critical to the functioning of the algorithm.@@@@1@25@@oe@19-8-2009
10010460@unknown@formal@none@1@S@Instructions are usually assumed to be listed explicitly, and are described as starting "from the top" and going "down to the bottom", an idea that is described more formally by ''[[control flow|flow of control]]''.@@@@1@34@@oe@19-8-2009
10010470@unknown@formal@none@1@S@So far, this discussion of the formalization of an algorithm has assumed the premises of [[imperative programming]].@@@@1@17@@oe@19-8-2009
10010480@unknown@formal@none@1@S@This is the most common conception, and it attempts to describe a task in discrete, "mechanical" means.@@@@1@17@@oe@19-8-2009
10010490@unknown@formal@none@1@S@Unique to this conception of formalized algorithms is the [[assignment operation]], setting the value of a variable.@@@@1@17@@oe@19-8-2009
10010500@unknown@formal@none@1@S@It derives from the intuition of "[[memory]]" as a scratchpad.@@@@1@10@@oe@19-8-2009
10010510@unknown@formal@none@1@S@There is an example below of such an assignment.@@@@1@9@@oe@19-8-2009
10010520@unknown@formal@none@1@S@For some alternate conceptions of what constitutes an algorithm see [[functional programming]] and [[logic programming]] .@@@@1@16@@oe@19-8-2009
10010530@unknown@formal@none@1@S@=== Termination ===@@@@1@3@@oe@19-8-2009
10010540@unknown@formal@none@1@S@Some writers restrict the definition of ''algorithm'' to procedures that eventually finish.@@@@1@12@@oe@19-8-2009
10010550@unknown@formal@none@1@S@In such a category Kleene places the "''decision procedure'' or ''decision method'' or ''algorithm'' for the question" (Kleene 1952:136).@@@@1@19@@oe@19-8-2009
10010560@unknown@formal@none@1@S@Others, including Kleene, include procedures that could run forever without stopping; such a procedure has been called a "computational method" (Knuth 1997:5) or "''calculation procedure'' or ''algorithm''" (Kleene 1952:137); however, Kleene notes that such a method must eventually exhibit "some object" (Kleene 1952:137).@@@@1@43@@oe@19-8-2009
10010570@unknown@formal@none@1@S@Minsky makes the pertinent observation, in regards to determining whether an algorithm will eventually terminate (from a particular starting state):@@@@1@20@@oe@19-8-2009
10010580@unknown@formal@none@1@S@<blockquote> But if the length of the process is not known in advance, then "trying" it may not be decisive, because if the process does go on forever — then at no time will we ever be sure of the answer (Minsky 1967:105).</blockquote>@@@@1@43@@oe@19-8-2009
10010590@unknown@formal@none@1@S@As it happens, no other method can do any better, as was shown by [[Alan Turing]] with his celebrated result on the undecidability of the so-called [[halting problem]].@@@@1@28@@oe@19-8-2009
10010600@unknown@formal@none@1@S@There is no algorithmic procedure for determining of arbitrary algorithms whether or not they terminate from given starting states.@@@@1@19@@oe@19-8-2009
10010610@unknown@formal@none@1@S@The analysis of algorithms for their likelihood of termination is called [[termination analysis]].@@@@1@13@@oe@19-8-2009
10010620@unknown@formal@none@1@S@See the examples of (im-)"proper" subtraction at [[partial function]] for more about what can happen when an algorithm fails for certain of its input numbers — e.g., (i) non-termination, (ii) production of "junk" (output in the wrong format to be considered a number) or no number(s) at all (halt ends the computation with no output), (iii) wrong number(s), or (iv) a combination of these.@@@@1@64@@oe@19-8-2009
10010630@unknown@formal@none@1@S@Kleene proposed that the production of "junk" or failure to produce a number is solved by having the algorithm detect these instances and produce e.g., an error message (he suggested "0"), or preferably, force the algorithm into an endless loop (Kleene 1952:322).@@@@1@42@@oe@19-8-2009
10010640@unknown@formal@none@1@S@Davis does this to his subtraction algorithm — he fixes his algorithm in a second example so that it is proper subtraction (Davis 1958:12-15).@@@@1@24@@oe@19-8-2009
10010650@unknown@formal@none@1@S@Along with the logical outcomes "true" and "false" Kleene also proposes the use of a third logical symbol "u" — undecided (Kleene 1952:326) — thus an algorithm will always produce ''something'' when confronted with a "proposition".@@@@1@36@@oe@19-8-2009
10010660@unknown@formal@none@1@S@The problem of wrong answers must be solved with an independent "proof" of the algorithm e.g., using induction:@@@@1@18@@oe@19-8-2009
10010670@unknown@formal@none@1@S@<blockquote> We normally require auxiliary evidence for this (that the algorithm correctly defines a [[mu recursive function]]), e.g., in the form of an inductive proof that, for each argument value, the computation terminates with a unique value (Minsky 1967:186).</blockquote>@@@@1@39@@oe@19-8-2009
10010680@unknown@formal@none@1@S@=== Expressing algorithms ===@@@@1@4@@oe@19-8-2009
10010690@unknown@formal@none@1@S@Algorithms can be expressed in many kinds of notation, including [[natural language]]s, [[pseudocode]], [[flowchart]]s, and [[programming language]]s.@@@@1@17@@oe@19-8-2009
10010700@unknown@formal@none@1@S@Natural language expressions of algorithms tend to be verbose and ambiguous, and are rarely used for complex or technical algorithms.@@@@1@20@@oe@19-8-2009
10010710@unknown@formal@none@1@S@Pseudocode and flowcharts are structured ways to express algorithms that avoid many of the ambiguities common in natural language statements, while remaining independent of a particular implementation language.@@@@1@28@@oe@19-8-2009
10010720@unknown@formal@none@1@S@Programming languages are primarily intended for expressing algorithms in a form that can be executed by a [[computer]], but are often used as a way to define or document algorithms.@@@@1@30@@oe@19-8-2009
10010730@unknown@formal@none@1@S@There is a wide variety of representations possible and one can express a given [[Turing machine]] program as a sequence of machine tables (see more at [[finite state machine]] and [[state transition table]]), as flowcharts (see more at [[state diagram]]), or as a form of rudimentary [[machine code]] or [[assembly code]] called "sets of quadruples" (see more at [[Turing machine]]).@@@@1@60@@oe@19-8-2009
10010740@unknown@formal@none@1@S@Sometimes it is helpful in the description of an algorithm to supplement small "flow charts" (state diagrams) with natural-language and/or arithmetic expressions written inside "[[block diagram]]s" to summarize what the "flow charts" are accomplishing.@@@@1@34@@oe@19-8-2009
10010750@unknown@formal@none@1@S@Representations of algorithms are generally classed into three accepted levels of Turing machine description (Sipser 2006:157):@@@@1@16@@oe@19-8-2009
10010760@unknown@formal@none@1@S@*'''1 High-level description''':@@@@1@3@@oe@19-8-2009
10010770@unknown@formal@none@1@S@:: "...prose to describe an algorithm, ignoring the implementation details.@@@@1@10@@oe@19-8-2009
10010780@unknown@formal@none@1@S@At this level we do not need to mention how the machine manages its tape or head"@@@@1@17@@oe@19-8-2009
10010790@unknown@formal@none@1@S@*'''2 Implementation description''':@@@@1@3@@oe@19-8-2009
10010800@unknown@formal@none@1@S@:: "...prose used to define the way the Turing machine uses its head and the way that it stores data on its tape.@@@@1@23@@oe@19-8-2009
10010810@unknown@formal@none@1@S@At this level we do not give details of states or transition function"@@@@1@13@@oe@19-8-2009
10010820@unknown@formal@none@1@S@*'''3 Formal description''':@@@@1@3@@oe@19-8-2009
10010830@unknown@formal@none@1@S@:: Most detailed, "lowest level", gives the Turing machine's "state table".@@@@1@11@@oe@19-8-2009
10010840@unknown@formal@none@1@S@:''For an example of the simple algorithm "Add m+n" described in all three levels see [[Algorithm examples]].''@@@@1@17@@oe@19-8-2009
10010850@unknown@formal@none@1@S@=== Implementation ===@@@@1@3@@oe@19-8-2009
10010860@unknown@formal@none@1@S@Most algorithms are intended to be implemented as [[computer programs]].@@@@1@10@@oe@19-8-2009
10010870@unknown@formal@none@1@S@However, algorithms are also implemented by other means, such as in a biological [[neural network]] (for example, the [[human brain]] implementing [[arithmetic]] or an insect looking for food), in an [[electrical circuit]], or in a mechanical device.@@@@1@37@@oe@19-8-2009
10010880@unknown@formal@none@1@S@== Example ==@@@@1@3@@oe@19-8-2009
10010890@unknown@formal@none@1@S@One of the simplest algorithms is to find the largest number in an (unsorted) list of numbers.@@@@1@17@@oe@19-8-2009
10010900@unknown@formal@none@1@S@The solution necessarily requires looking at every number in the list, but only once at each.@@@@1@16@@oe@19-8-2009
10010910@unknown@formal@none@1@S@From this follows a simple algorithm, which can be stated in a high-level description [[English language|English]] prose, as:@@@@1@18@@oe@19-8-2009
10010920@unknown@formal@none@1@S@'''High-level description:'''@@@@1@2@@oe@19-8-2009
10010930@unknown@formal@none@1@S@# Assume the first item is largest.@@@@1@7@@oe@19-8-2009
10010940@unknown@formal@none@1@S@# Look at each of the remaining items in the list and if it is larger than the largest item so far, make a note of it.@@@@1@27@@oe@19-8-2009
10010950@unknown@formal@none@1@S@# The last noted item is the largest in the list when the process is complete.@@@@1@16@@oe@19-8-2009
10010960@unknown@formal@none@1@S@'''(Quasi-)formal description:''' Written in prose but much closer to the high-level language of a computer program, the following is the more formal coding of the algorithm in [[pseudocode]] or [[pidgin code]]:@@@@1@31@@oe@19-8-2009
10010970@unknown@formal@none@1@S@Input: A non-empty list of numbers ''L''.@@@@1@7@@oe@19-8-2009
10010980@unknown@formal@none@1@S@Output: The ''largest'' number in the list ''L''. ''largest'' ← ''L''<sub>0</sub> '''for each''' ''item'' '''in''' the list ''L<sub>≥1</sub>'', '''do''' '''if''' the ''item'' > ''largest'', '''then''' ''largest'' ← the ''item'' '''return''' ''largest''@@@@1@31@@oe@19-8-2009
10010990@unknown@formal@none@1@S@For a more complex example of an algorithm, see [[Euclid's algorithm]] for the [[greatest common divisor]], one of the earliest algorithms known.@@@@1@22@@oe@19-8-2009
10011000@unknown@formal@none@1@S@=== Algorithm analysis ===@@@@1@4@@oe@19-8-2009
10011010@unknown@formal@none@1@S@As it happens, it is important to know how much of a particular resource (such as time or storage) is required for a given algorithm.@@@@1@25@@oe@19-8-2009
10011020@unknown@formal@none@1@S@Methods have been developed for the [[analysis of algorithms]] to obtain such quantitative answers; for example, the algorithm above has a time requirement of O(''n''), using the [[big O notation]] with ''n'' as the length of the list.@@@@1@38@@oe@19-8-2009
10011030@unknown@formal@none@1@S@At all times the algorithm only needs to remember two values: the largest number found so far, and its current position in the input list.@@@@1@25@@oe@19-8-2009
10011040@unknown@formal@none@1@S@Therefore it is said to have a space requirement of ''O(1)'', if the space required to store the input numbers is not counted, or O (log ''n'') if it is counted.@@@@1@31@@oe@19-8-2009
10011050@unknown@formal@none@1@S@Different algorithms may complete the same task with a different set of instructions in less or more time, space, or effort than others.@@@@1@23@@oe@19-8-2009
10011060@unknown@formal@none@1@S@For example, given two different recipes for making potato salad, one may have ''peel the potato'' before ''boil the potato'' while the other presents the steps in the reverse order, yet they both call for these steps to be repeated for all potatoes and end when the potato salad is ready to be eaten.@@@@1@54@@oe@19-8-2009
10011070@unknown@formal@none@1@S@The [[analysis of algorithms|analysis and study of algorithms]] is a discipline of [[computer science]], and is often practiced abstractly without the use of a specific [[programming language]] or implementation.@@@@1@29@@oe@19-8-2009
10011080@unknown@formal@none@1@S@In this sense, algorithm analysis resembles other mathematical disciplines in that it focuses on the underlying properties of the algorithm and not on the specifics of any particular implementation.@@@@1@29@@oe@19-8-2009
10011090@unknown@formal@none@1@S@Usually [[pseudocode]] is used for analysis as it is the simplest and most general representation.@@@@1@15@@oe@19-8-2009
10011100@unknown@formal@none@1@S@== Classes ==@@@@1@3@@oe@19-8-2009
10011110@unknown@formal@none@1@S@There are various ways to classify algorithms, each with its own merits.@@@@1@12@@oe@19-8-2009
10011120@unknown@formal@none@1@S@=== Classification by implementation ===@@@@1@5@@oe@19-8-2009
10011130@unknown@formal@none@1@S@One way to classify algorithms is by implementation means.@@@@1@9@@oe@19-8-2009
10011140@unknown@formal@none@1@S@* '''Recursion''' or '''iteration''': A [[recursive algorithm]] is one that invokes (makes reference to) itself repeatedly until a certain condition matches, which is a method common to [[functional programming]].@@@@1@29@@oe@19-8-2009
10011150@unknown@formal@none@1@S@[[Iteration|Iterative]] algorithms use repetitive constructs like [[Control flow#Loops|loops]] and sometimes additional data structures like [[Stack (data structure)|stacks]] to solve the given problems.@@@@1@22@@oe@19-8-2009
10011160@unknown@formal@none@1@S@Some problems are naturally suited for one implementation or the other.@@@@1@11@@oe@19-8-2009
10011170@unknown@formal@none@1@S@For example, [[towers of hanoi]] is well understood in recursive implementation.@@@@1@11@@oe@19-8-2009
10011180@unknown@formal@none@1@S@Every recursive version has an equivalent (but possibly more or less complex) iterative version, and vice versa.@@@@1@17@@oe@19-8-2009
10011190@unknown@formal@none@1@S@* '''Logical''': An algorithm may be viewed as controlled [[Deductive reasoning|logical deduction]].@@@@1@12@@oe@19-8-2009
10011200@unknown@formal@none@1@S@This notion may be expressed as: '''Algorithm = logic + control''' (Kowalski 1979).@@@@1@13@@oe@19-8-2009
10011210@unknown@formal@none@1@S@The logic component expresses the axioms that may be used in the computation and the control component determines the way in which deduction is applied to the axioms.@@@@1@28@@oe@19-8-2009
10011220@unknown@formal@none@1@S@This is the basis for the [[logic programming]] paradigm.@@@@1@9@@oe@19-8-2009
10011230@unknown@formal@none@1@S@In pure logic programming languages the control component is fixed and algorithms are specified by supplying only the logic component.@@@@1@20@@oe@19-8-2009
10011240@unknown@formal@none@1@S@The appeal of this approach is the elegant [[Formal semantics of programming languages|semantics]]: a change in the axioms has a well defined change in the algorithm.@@@@1@26@@oe@19-8-2009
10011250@unknown@formal@none@1@S@* '''Serial''' or '''parallel''' or '''distributed''': Algorithms are usually discussed with the assumption that computers execute one instruction of an algorithm at a time.@@@@1@24@@oe@19-8-2009
10011260@unknown@formal@none@1@S@Those computers are sometimes called serial computers.@@@@1@7@@oe@19-8-2009
10011270@unknown@formal@none@1@S@An algorithm designed for such an environment is called a serial algorithm, as opposed to [[parallel algorithm]]s or [[distributed algorithms]].@@@@1@20@@oe@19-8-2009
10011280@unknown@formal@none@1@S@Parallel algorithms take advantage of computer architectures where several processors can work on a problem at the same time, whereas distributed algorithms utilize multiple machines connected with a [[Computer Network|network]].@@@@1@30@@oe@19-8-2009
10011290@unknown@formal@none@1@S@Parallel or distributed algorithms divide the problem into more symmetrical or asymmetrical subproblems and collect the results back together.@@@@1@19@@oe@19-8-2009
10011300@unknown@formal@none@1@S@The resource consumption in such algorithms is not only processor cycles on each processor but also the communication overhead between the processors.@@@@1@22@@oe@19-8-2009
10011310@unknown@formal@none@1@S@Sorting algorithms can be parallelized efficiently, but their communication overhead is expensive.@@@@1@12@@oe@19-8-2009
10011320@unknown@formal@none@1@S@Iterative algorithms are generally parallelizable.@@@@1@5@@oe@19-8-2009
10011330@unknown@formal@none@1@S@Some problems have no parallel algorithms, and are called inherently serial problems.@@@@1@12@@oe@19-8-2009
10011340@unknown@formal@none@1@S@* '''Deterministic''' or '''non-deterministic''': [[Deterministic algorithm]]s solve the problem with exact decision at every step of the algorithm whereas [[non-deterministic algorithm]] solve problems via guessing although typical guesses are made more accurate through the use of [[heuristics]].@@@@1@37@@oe@19-8-2009
10011350@unknown@formal@none@1@S@* '''Exact''' or '''approximate''': While many algorithms reach an exact solution, [[approximation algorithm]]s seek an approximation that is close to the true solution.@@@@1@23@@oe@19-8-2009
10011360@unknown@formal@none@1@S@Approximation may use either a deterministic or a random strategy.@@@@1@10@@oe@19-8-2009
10011370@unknown@formal@none@1@S@Such algorithms have practical value for many hard problems.@@@@1@9@@oe@19-8-2009
10011380@unknown@formal@none@1@S@=== Classification by design paradigm ===@@@@1@6@@oe@19-8-2009
10011390@unknown@formal@none@1@S@Another way of classifying algorithms is by their design methodology or paradigm.@@@@1@12@@oe@19-8-2009
10011400@unknown@formal@none@1@S@There is a certain number of paradigms, each different from the other.@@@@1@12@@oe@19-8-2009
10011410@unknown@formal@none@1@S@Furthermore, each of these categories will include many different types of algorithms.@@@@1@12@@oe@19-8-2009
10011420@unknown@formal@none@1@S@Some commonly found paradigms include:@@@@1@5@@oe@19-8-2009
10011430@unknown@formal@none@1@S@* '''Divide and conquer'''.@@@@1@4@@oe@19-8-2009
10011440@unknown@formal@none@1@S@A [[divide and conquer algorithm]] repeatedly reduces an instance of a problem to one or more smaller instances of the same problem (usually [[recursion|recursively]]), until the instances are small enough to solve easily.@@@@1@33@@oe@19-8-2009
10011450@unknown@formal@none@1@S@One such example of divide and conquer is [[mergesort|merge sorting]].@@@@1@10@@oe@19-8-2009
10011460@unknown@formal@none@1@S@Sorting can be done on each segment of data after dividing data into segments and sorting of entire data can be obtained in conquer phase by merging them.@@@@1@28@@oe@19-8-2009
10011470@unknown@formal@none@1@S@A simpler variant of divide and conquer is called '''decrease and conquer algorithm''', that solves an identical subproblem and uses the solution of this subproblem to solve the bigger problem.@@@@1@30@@oe@19-8-2009
10011480@unknown@formal@none@1@S@Divide and conquer divides the problem into multiple subproblems and so conquer stage will be more complex than decrease and conquer algorithms.@@@@1@22@@oe@19-8-2009
10011490@unknown@formal@none@1@S@An example of decrease and conquer algorithm is [[binary search algorithm]].@@@@1@11@@oe@19-8-2009
10011500@unknown@formal@none@1@S@* '''[[Dynamic programming]]'''.@@@@1@3@@oe@19-8-2009
10011510@unknown@formal@none@1@S@When a problem shows [[optimal substructure]], meaning the optimal solution to a problem can be constructed from optimal solutions to subproblems, and [[overlapping subproblems]], meaning the same subproblems are used to solve many different problem instances, a quicker approach called ''dynamic programming'' avoids recomputing solutions that have already been computed.@@@@1@50@@oe@19-8-2009
10011520@unknown@formal@none@1@S@For example, the shortest path to a goal from a vertex in a weighted [[graph (mathematics)|graph]] can be found by using the shortest path to the goal from all adjacent vertices.@@@@1@31@@oe@19-8-2009
10011530@unknown@formal@none@1@S@Dynamic programming and [[memoization]] go together.@@@@1@6@@oe@19-8-2009
10011540@unknown@formal@none@1@S@The main difference between dynamic programming and divide and conquer is that subproblems are more or less independent in divide and conquer, whereas subproblems overlap in dynamic programming.@@@@1@28@@oe@19-8-2009
10011550@unknown@formal@none@1@S@The difference between dynamic programming and straightforward recursion is in caching or memoization of recursive calls.@@@@1@16@@oe@19-8-2009
10011560@unknown@formal@none@1@S@When subproblems are independent and there is no repetition, memoization does not help; hence dynamic programming is not a solution for all complex problems.@@@@1@24@@oe@19-8-2009
10011570@unknown@formal@none@1@S@By using memoization or maintaining a [[Mathematical table|table]] of subproblems already solved, dynamic programming reduces the exponential nature of many problems to polynomial complexity.@@@@1@24@@oe@19-8-2009
10011580@unknown@formal@none@1@S@* '''The greedy method'''.@@@@1@4@@oe@19-8-2009
10011590@unknown@formal@none@1@S@A [[greedy algorithm]] is similar to a [[dynamic programming|dynamic programming algorithm]], but the difference is that solutions to the subproblems do not have to be known at each stage; instead a "greedy" choice can be made of what looks best for the moment.@@@@1@43@@oe@19-8-2009
10011600@unknown@formal@none@1@S@The greedy method extends the solution with the best possible decision (not all feasible decisions) at an algorithmic stage based on the current local optimum and the best decision (not all possible decisions) made in previous stage.@@@@1@37@@oe@19-8-2009
10011610@unknown@formal@none@1@S@It is not exhaustive, and does not give accurate answer to many problems.@@@@1@13@@oe@19-8-2009
10011620@unknown@formal@none@1@S@But when it works, it will be the fastest method.@@@@1@10@@oe@19-8-2009
10011630@unknown@formal@none@1@S@The most popular greedy algorithm is finding the minimal spanning tree as given by [[kruskal's algorithm|Kruskal]].@@@@1@16@@oe@19-8-2009
10011640@unknown@formal@none@1@S@* '''Linear programming'''.@@@@1@3@@oe@19-8-2009
10011650@unknown@formal@none@1@S@When solving a problem using [[linear programming]], specific [[inequality|inequalities]] involving the inputs are found and then an attempt is made to maximize (or minimize) some linear function of the inputs.@@@@1@30@@oe@19-8-2009
10011660@unknown@formal@none@1@S@Many problems (such as the [[Maximum flow problem|maximum flow]] for directed [[graph (mathematics)|graphs]]) can be stated in a linear programming way, and then be solved by a 'generic' algorithm such as the [[simplex algorithm]].@@@@1@34@@oe@19-8-2009
10011670@unknown@formal@none@1@S@A more complex variant of linear programming is called integer programming, where the solution space is restricted to the [[integers]].@@@@1@20@@oe@19-8-2009
10011680@unknown@formal@none@1@S@* '''[[Reduction (complexity)|Reduction]]'''.@@@@1@3@@oe@19-8-2009
10011690@unknown@formal@none@1@S@This technique involves solving a difficult problem by transforming it into a better known problem for which we have (hopefully) [[asymptotically optimal]] algorithms.@@@@1@23@@oe@19-8-2009
10011700@unknown@formal@none@1@S@The goal is to find a reducing algorithm whose [[Computational complexity theory|complexity]] is not dominated by the resulting reduced algorithm's.@@@@1@20@@oe@19-8-2009
10011710@unknown@formal@none@1@S@For example, one [[selection algorithm]] for finding the median in an unsorted list involves first sorting the list (the expensive portion) and then pulling out the middle element in the sorted list (the cheap portion).@@@@1@35@@oe@19-8-2009
10011720@unknown@formal@none@1@S@This technique is also known as ''transform and conquer''.@@@@1@9@@oe@19-8-2009
10011730@unknown@formal@none@1@S@* '''Search and enumeration'''.@@@@1@4@@oe@19-8-2009
10011740@unknown@formal@none@1@S@Many problems (such as playing [[chess]]) can be modeled as problems on [[graph theory|graphs]].@@@@1@14@@oe@19-8-2009
10011750@unknown@formal@none@1@S@A [[graph exploration algorithm]] specifies rules for moving around a graph and is useful for such problems.@@@@1@17@@oe@19-8-2009
10011760@unknown@formal@none@1@S@This category also includes [[search algorithm]]s, [[branch and bound]] enumeration and [[backtracking]].@@@@1@12@@oe@19-8-2009
10011770@unknown@formal@none@1@S@* '''The probabilistic and heuristic paradigm'''.@@@@1@6@@oe@19-8-2009
10011780@unknown@formal@none@1@S@Algorithms belonging to this class fit the definition of an algorithm more loosely.@@@@1@13@@oe@19-8-2009
10011790@unknown@formal@none@1@S@# [[Probabilistic algorithm]]s are those that make some choices randomly (or pseudo-randomly); for some problems, it can in fact be proven that the fastest solutions must involve some [[randomness]].@@@@1@29@@oe@19-8-2009
10011800@unknown@formal@none@1@S@# [[Genetic algorithm]]s attempt to find solutions to problems by mimicking biological [[evolution]]ary processes, with a cycle of random mutations yielding successive generations of "solutions".@@@@1@25@@oe@19-8-2009
10011810@unknown@formal@none@1@S@Thus, they emulate reproduction and "survival of the fittest".@@@@1@9@@oe@19-8-2009
10011820@unknown@formal@none@1@S@In [[genetic programming]], this approach is extended to algorithms, by regarding the algorithm itself as a "solution" to a problem.@@@@1@20@@oe@19-8-2009
10011830@unknown@formal@none@1@S@# [[Heuristic]] algorithms, whose general purpose is not to find an optimal solution, but an approximate solution where the time or resources are limited.@@@@1@24@@oe@19-8-2009
10011840@unknown@formal@none@1@S@They are not practical to find perfect solutions.@@@@1@8@@oe@19-8-2009
10011850@unknown@formal@none@1@S@An example of this would be [[local search (optimization)|local search]], [[tabu search]], or [[simulated annealing]] algorithms, a class of heuristic probabilistic algorithms that vary the solution of a problem by a random amount.@@@@1@33@@oe@19-8-2009
10011860@unknown@formal@none@1@S@The name "[[simulated annealing]]" alludes to the metallurgic term meaning the heating and cooling of metal to achieve freedom from defects.@@@@1@21@@oe@19-8-2009
10011870@unknown@formal@none@1@S@The purpose of the random variance is to find close to globally optimal solutions rather than simply locally optimal ones, the idea being that the random element will be decreased as the algorithm settles down to a solution.@@@@1@38@@oe@19-8-2009
10011880@unknown@formal@none@1@S@=== Classification by field of study ===@@@@1@7@@oe@19-8-2009
10011890@unknown@formal@none@1@S@Every field of science has its own problems and needs efficient algorithms.@@@@1@12@@oe@19-8-2009
10011900@unknown@formal@none@1@S@Related problems in one field are often studied together.@@@@1@9@@oe@19-8-2009
10011910@unknown@formal@none@1@S@Some example classes are [[search algorithm]]s, [[sorting algorithm]]s, [[merge algorithm]]s, [[numerical analysis|numerical algorithms]], [[graph theory|graph algorithms]], [[string algorithms]], [[computational geometry|computational geometric algorithms]], [[combinatorial|combinatorial algorithms]], [[machine learning]], [[cryptography]], [[data compression]] algorithms and [[parsing|parsing techniques]].@@@@1@33@@oe@19-8-2009
10011920@unknown@formal@none@1@S@Fields tend to overlap with each other, and algorithm advances in one field may improve those of other, sometimes completely unrelated, fields.@@@@1@22@@oe@19-8-2009
10011930@unknown@formal@none@1@S@For example, dynamic programming was originally invented for optimization of resource consumption in industry, but is now used in solving a broad range of problems in many fields.@@@@1@28@@oe@19-8-2009
10011940@unknown@formal@none@1@S@=== Classification by complexity ===@@@@1@5@@oe@19-8-2009
10011950@unknown@formal@none@1@S@Algorithms can be classified by the amount of time they need to complete compared to their input size.@@@@1@18@@oe@19-8-2009
10011960@unknown@formal@none@1@S@There is a wide variety: some algorithms complete in linear time relative to input size, some do so in an exponential amount of time or even worse, and some never halt.@@@@1@31@@oe@19-8-2009
10011970@unknown@formal@none@1@S@Additionally, some problems may have multiple algorithms of differing complexity, while other problems might have no algorithms or no known efficient algorithms.@@@@1@22@@oe@19-8-2009
10011980@unknown@formal@none@1@S@There are also mappings from some problems to other problems.@@@@1@10@@oe@19-8-2009
10011990@unknown@formal@none@1@S@Owing to this, it was found to be more suitable to classify the problems themselves instead of the algorithms into equivalence classes based on the complexity of the best possible algorithms for them.@@@@1@33@@oe@19-8-2009
10012000@unknown@formal@none@1@S@=== Classification by computing power ===@@@@1@6@@oe@19-8-2009
10012010@unknown@formal@none@1@S@Another way to classify algorithms is by computing power.@@@@1@9@@oe@19-8-2009
10012020@unknown@formal@none@1@S@This is typically done by considering some collection (class) of algorithms.@@@@1@11@@oe@19-8-2009
10012030@unknown@formal@none@1@S@A recursive class of algorithms is one that includes algorithms for all Turing computable functions.@@@@1@15@@oe@19-8-2009
10012040@unknown@formal@none@1@S@Looking at classes of algorithms allows for the possibility of restricting the available computational resources (time and memory) used in a computation.@@@@1@22@@oe@19-8-2009
10012050@unknown@formal@none@1@S@A subrecursive class of algorithms is one in which not all Turing computable functions can be obtained.@@@@1@17@@oe@19-8-2009
10012060@unknown@formal@none@1@S@For example, the algorithms that run in [[P (complexity)|polynomial time]] suffice for many important types of computation but do not exhaust all Turing computable functions.@@@@1@25@@oe@19-8-2009
10012070@unknown@formal@none@1@S@The class algorithms implemented by [[primitive recursive function]]s is another subrecursive class.@@@@1@12@@oe@19-8-2009
10012080@unknown@formal@none@1@S@Burgin (2005, p. 24) uses a generalized definition of algorithms that relaxes the common requirement that the output of the algorithm that computes a function must be determined after a finite number of steps.@@@@1@34@@oe@19-8-2009
10012090@unknown@formal@none@1@S@He defines a super-recursive class of algorithms as "a class of algorithms in which it is possible to compute functions not computable by any Turing machine" (Burgin 2005, p. 107).@@@@1@30@@oe@19-8-2009
10012100@unknown@formal@none@1@S@This is closely related to the study of methods of [[hypercomputation]].@@@@1@11@@oe@19-8-2009
10012110@unknown@formal@none@1@S@== Legal issues ==@@@@1@4@@oe@19-8-2009
10012120@unknown@formal@none@1@S@:''See also: [[Software patents]] for a general overview of the patentability of software, including computer-implemented algorithms.''@@@@1@16@@oe@19-8-2009
10012130@unknown@formal@none@1@S@Algorithms, by themselves, are not usually patentable.@@@@1@7@@oe@19-8-2009
10012140@unknown@formal@none@1@S@In the [[United States]], a claim consisting solely of simple manipulations of abstract concepts, numbers, or signals do not constitute "processes" (USPTO 2006) and hence algorithms are not patentable (as in [[Gottschalk v. Benson]]).@@@@1@34@@oe@19-8-2009
10012150@unknown@formal@none@1@S@However, practical applications of algorithms are sometimes patentable.@@@@1@8@@oe@19-8-2009
10012160@unknown@formal@none@1@S@For example, in [[Diamond v. Diehr]], the application of a simple [[feedback]] algorithm to aid in the curing of [[synthetic rubber]] was deemed patentable.@@@@1@24@@oe@19-8-2009
10012170@unknown@formal@none@1@S@The [[Software patent debate|patenting of software]] is highly controversial, and there are highly criticized patents involving algorithms, especially [[data compression]] algorithms, such as [[Unisys]]' [[Graphics Interchange Format#Unisys and LZW patent enforcement|LZW patent]].@@@@1@32@@oe@19-8-2009
10012180@unknown@formal@none@1@S@Additionally, some cryptographic algorithms have export restrictions (see [[export of cryptography]]).@@@@1@11@@oe@19-8-2009
10012190@unknown@formal@none@1@S@== History: Development of the notion of "algorithm" ==@@@@1@9@@oe@19-8-2009
10012200@unknown@formal@none@1@S@=== Origin of the word ===@@@@1@6@@oe@19-8-2009
10012210@unknown@formal@none@1@S@The word ''algorithm'' comes from the name of the 9th century [[Persian people|Persian]] mathematician [[al-Khwarizmi|Abu Abdullah Muhammad ibn Musa al-Khwarizmi]] whose works introduced Indian numerals and algebraic concepts.@@@@1@28@@oe@19-8-2009
10012220@unknown@formal@none@1@S@He worked in [[Baghdad]] at the time when it was the centre of scientific studies and trade.@@@@1@17@@oe@19-8-2009
10012230@unknown@formal@none@1@S@The word ''[[algorism]]'' originally referred only to the rules of performing [[arithmetic]] using [[Hindu-Arabic numeral system|Arabic numerals]] but evolved via European Latin translation of al-Khwarizmi's name into ''algorithm'' by the 18th century.@@@@1@32@@oe@19-8-2009
10012240@unknown@formal@none@1@S@The word evolved to include all definite procedures for solving problems or performing tasks.@@@@1@14@@oe@19-8-2009
10012250@unknown@formal@none@1@S@=== Discrete and distinguishable symbols ===@@@@1@6@@oe@19-8-2009
10012260@unknown@formal@none@1@S@'''Tally-marks''': To keep track of their flocks, their sacks of grain and their money the ancients used tallying: accumulating stones or marks scratched on sticks, or making discrete symbols in clay.@@@@1@31@@oe@19-8-2009
10012270@unknown@formal@none@1@S@Through the Babylonian and Egyptian use of marks and symbols, eventually [[Roman numerals]] and the [[abacus]] evolved (Dilson, p.16–41).@@@@1@19@@oe@19-8-2009
10012280@unknown@formal@none@1@S@Tally marks appear prominently in [[unary numeral system]] arithmetic used in [[Turing machine]] and [[Post-Turing machine]] computations.@@@@1@17@@oe@19-8-2009
10012290@unknown@formal@none@1@S@=== Manipulation of symbols as "place holders" for numbers: algebra ===@@@@1@11@@oe@19-8-2009
10012300@unknown@formal@none@1@S@The work of the Ancient Greek geometers, Persian mathematician [[Al-Khwarizmi]] (often considered as the "father of [[algebra]]"), and Western European mathematicians culminated in [[Leibniz]]'s notion of the [[calculus ratiocinator]] (ca 1680):@@@@1@31@@oe@19-8-2009
10012310@unknown@formal@none@1@S@:"A good century and a half ahead of his time, Leibniz proposed an algebra of logic, an algebra that would specify the rules for manipulating logical concepts in the manner that ordinary algebra specifies the rules for manipulating numbers" (Davis 2000:1)@@@@1@41@@oe@19-8-2009
10012320@unknown@formal@none@1@S@=== Mechanical contrivances with discrete states ===@@@@1@7@@oe@19-8-2009
10012330@unknown@formal@none@1@S@'''The clock''': Bolter credits the invention of the weight-driven [[clock]] as “The key invention [of Europe in the Middle Ages]", in particular the [[verge escapement]]< (Bolter 1984:24) that provides us with the tick and tock of a mechanical clock.@@@@1@39@@oe@19-8-2009
10012340@unknown@formal@none@1@S@“The accurate automatic machine” (Bolter 1984:26) led immediately to "mechanical [[automata]]" beginning in the thirteenth century and finally to “computational machines" – the [[difference engine]] and [[analytical engine]]s of [[Charles Babbage]] and Countess [[Ada Lovelace]] (Bolter p.33–34, p.204–206).@@@@1@38@@oe@19-8-2009
10012350@unknown@formal@none@1@S@'''Jacquard loom, Hollerith punch cards, telegraphy and telephony — the electromechanical relay''': Bell and Newell (1971) indicate that the [[Jacquard loom]] (1801), precursor to [[Hollerith cards]] (punch cards, 1887), and “telephone switching technologies” were the roots of a tree leading to the development of the first computers (Bell and Newell diagram p. 39, cf Davis 2000).@@@@1@56@@oe@19-8-2009
10012360@unknown@formal@none@1@S@By the mid-1800s the [[telegraph]], the precursor of the telephone, was in use throughout the world, its discrete and distinguishable encoding of letters as “dots and dashes” a common sound.@@@@1@30@@oe@19-8-2009
10012370@unknown@formal@none@1@S@By the late 1800s the [[ticker tape]] (ca 1870s) was in use, as was the use of [[Hollerith cards]] in the 1890 U.S. census.@@@@1@24@@oe@19-8-2009
10012380@unknown@formal@none@1@S@Then came the [[Teletype]] (ca 1910) with its punched-paper use of [[Baudot code]] on tape.@@@@1@15@@oe@19-8-2009
10012390@unknown@formal@none@1@S@Telephone-switching networks of electromechanical [[relay]]s (invented 1835) was behind the work of [[George Stibitz]] (1937), the inventor of the digital adding device.@@@@1@22@@oe@19-8-2009
10012400@unknown@formal@none@1@S@As he worked in Bell Laboratories, he observed the “burdensome’ use of mechanical calculators with gears.@@@@1@16@@oe@19-8-2009
10012410@unknown@formal@none@1@S@"He went home one evening in 1937 intending to test his idea....@@@@1@12@@oe@19-8-2009
10012420@unknown@formal@none@1@S@When the tinkering was over, Stibitz had constructed a binary adding device".@@@@1@12@@oe@19-8-2009
10012430@unknown@formal@none@1@S@(Valley News, p. 13).@@@@1@4@@oe@19-8-2009
10012440@unknown@formal@none@1@S@Davis (2000) observes the particular importance of the electromechanical relay (with its two "binary states" ''open'' and ''closed''):@@@@1@18@@oe@19-8-2009
10012450@unknown@formal@none@1@S@: It was only with the development, beginning in the 1930s, of electromechanical calculators using electrical relays, that machines were built having the scope Babbage had envisioned."@@@@1@27@@oe@19-8-2009
10012460@unknown@formal@none@1@S@(Davis, p. 14).@@@@1@3@@oe@19-8-2009
10012470@unknown@formal@none@1@S@=== Mathematics during the 1800s up to the mid-1900s ===@@@@1@10@@oe@19-8-2009
10012480@unknown@formal@none@1@S@'''Symbols and rules''': In rapid succession the mathematics of [[George Boole]] (1847, 1854), [[Gottlob Frege]] (1879), and [[Giuseppe Peano]] (1888–1889) reduced arithmetic to a sequence of symbols manipulated by rules.@@@@1@30@@oe@19-8-2009
10012490@unknown@formal@none@1@S@Peano's ''The principles of arithmetic, presented by a new method'' (1888) was "the first attempt at an axiomatization of mathematics in a symbolic language" (van Heijenoort:81ff).@@@@1@26@@oe@19-8-2009
10012500@unknown@formal@none@1@S@But Heijenoort gives Frege (1879) this kudos: Frege’s is "perhaps the most important single work ever written in logic. ... in which we see a " 'formula language', that is a ''lingua characterica'', a language written with special symbols, "for pure thought", that is, free from rhetorical embellishments ... constructed from specific symbols that are manipulated according to definite rules" (van Heijenoort:1).@@@@1@62@@oe@19-8-2009
10012510@unknown@formal@none@1@S@The work of Frege was further simplified and amplified by [[Alfred North Whitehead]] and [[Bertrand Russell]] in their [[Principia Mathematica]] (1910–1913).@@@@1@21@@oe@19-8-2009
10012520@unknown@formal@none@1@S@'''The paradoxes''': At the same time a number of disturbing paradoxes appeared in the literature, in particular the [[Burali-Forti paradox]] (1897), the [[Russell paradox]] (1902–03), and the [[Richard Paradox]] (Dixon 1906, cf Kleene 1952:36–40).@@@@1@34@@oe@19-8-2009
10012530@unknown@formal@none@1@S@The resultant considerations led to [[Kurt Gödel]]’s paper (1931) — he specifically cites the paradox of the liar — that completely reduces rules of [[recursion]] to numbers.@@@@1@27@@oe@19-8-2009
10012540@unknown@formal@none@1@S@'''Effective calculability''': In an effort to solve the [[Entscheidungsproblem]] defined precisely by Hilbert in 1928, mathematicians first set about to define what was meant by an "effective method" or "effective calculation" or "effective calculability" (i.e., a calculation that would succeed).@@@@1@40@@oe@19-8-2009
10012550@unknown@formal@none@1@S@In rapid succession the following appeared: [[Alonzo Church]], [[Stephen Kleene]] and [[J.B. Rosser]]'s [[λ-calculus]], (cf footnote in [[Alonzo Church]] 1936a:90, 1936b:110) a finely-honed definition of "general recursion" from the work of Gödel acting on suggestions of [[Jacques Herbrand]] (cf Gödel's Princeton lectures of 1934) and subsequent simplifications by Kleene (1935-6:237ff, 1943:255ff). Church's proof (1936:88ff) that the [[Entscheidungsproblem]] was unsolvable, [[Emil Post]]'s definition of effective calculability as a worker mindlessly following a list of instructions to move left or right through a sequence of rooms and while there either mark or erase a paper or observe the paper and make a yes-no decision about the next instruction (cf "Formulation I", Post 1936:289-290).@@@@1@111@@oe@19-8-2009
10012560@unknown@formal@none@1@S@[[Alan Turing]]'s proof of that the Entscheidungsproblem was unsolvable by use of his "a- [automatic-] machine"(Turing 1936-7:116ff) -- in effect almost identical to Post's "formulation", [[J. Barkley Rosser]]'s definition of "effective method" in terms of "a machine" (Rosser 1939:226).@@@@1@39@@oe@19-8-2009
10012570@unknown@formal@none@1@S@[[S. C. Kleene]]'s proposal of a precursor to "[[Church thesis]]" that he called "Thesis I" (Kleene 1943:273–274), and a few years later Kleene's renaming his Thesis "Church's Thesis" (Kleene 1952:300, 317) and proposing "Turing's Thesis" (Kleene 1952:376).@@@@1@37@@oe@19-8-2009
10012580@unknown@formal@none@1@S@=== Emil Post (1936) and Alan Turing (1936-7, 1939)===@@@@1@9@@oe@19-8-2009
10012590@unknown@formal@none@1@S@Here is a remarkable coincidence of two men not knowing each other but describing a process of men-as-computers working on computations — and they yield virtually identical definitions.@@@@1@28@@oe@19-8-2009
10012600@unknown@formal@none@1@S@[[Emil Post]] (1936) described the actions of a "computer" (human being) as follows:@@@@1@13@@oe@19-8-2009
10012610@unknown@formal@none@1@S@:"...two concepts are involved: that of a ''symbol space'' in which the work leading from problem to answer is to be carried out, and a fixed unalterable ''set of directions''.@@@@1@30@@oe@19-8-2009
10012620@unknown@formal@none@1@S@His symbol space would be@@@@1@5@@oe@19-8-2009
10012630@unknown@formal@none@1@S@:"a two way infinite sequence of spaces or boxes...@@@@1@9@@oe@19-8-2009
10012640@unknown@formal@none@1@S@The problem solver or worker is to move and work in this symbol space, being capable of being in, and operating in but one box at a time.... a box is to admit of but two possible conditions, i.e., being empty or unmarked, and having a single mark in it, say a vertical stroke.@@@@1@54@@oe@19-8-2009
10012650@unknown@formal@none@1@S@:"One box is to be singled out and called the starting point. ...a specific problem is to be given in symbolic form by a finite number of boxes [i.e., INPUT] being marked with a stroke.@@@@1@35@@oe@19-8-2009
10012660@unknown@formal@none@1@S@Likewise the answer [i.e., OUTPUT] is to be given in symbolic form by such a configuration of marked boxes....@@@@1@19@@oe@19-8-2009
10012670@unknown@formal@none@1@S@:"A set of directions applicable to a general problem sets up a deterministic process when applied to each specific problem.@@@@1@20@@oe@19-8-2009
10012680@unknown@formal@none@1@S@This process will terminate only when it comes to the direction of type (C ) [i.e., STOP]." (U p. 289–290)@@@@1@20@@oe@19-8-2009
10012685@unknown@formal@none@1@S@See more at [[Post-Turing machine]]@@@@1@5@@oe@19-8-2009
10012690@unknown@formal@none@1@S@[[Alan Turing]]’s work (1936, 1939:160) preceded that of Stibitz (1937); it is unknown whether Stibitz knew of the work of Turing.@@@@1@21@@oe@19-8-2009
10012700@unknown@formal@none@1@S@Turing’s biographer believed that Turing’s use of a typewriter-like model derived from a youthful interest: “Alan had dreamt of inventing typewriters as a boy; Mrs. Turing had a typewriter; and he could well have begun by asking himself what was meant by calling a typewriter 'mechanical'" (Hodges, p. 96).@@@@1@49@@oe@19-8-2009
10012710@unknown@formal@none@1@S@Given the prevalence of Morse code and telegraphy, ticker tape machines, and Teletypes we might conjecture that all were influences.@@@@1@20@@oe@19-8-2009
10012720@unknown@formal@none@1@S@Turing — his model of computation is now called a [[Turing machine]] — begins, as did Post, with an analysis of a human computer that he whittles down to a simple set of basic motions and "states of mind".@@@@1@39@@oe@19-8-2009
10012730@unknown@formal@none@1@S@But he continues a step further and creates a machine as a model of computation of numbers (Turing 1936-7:116).@@@@1@19@@oe@19-8-2009
10012740@unknown@formal@none@1@S@:"Computing is normally done by writing certain symbols on paper.@@@@1@10@@oe@19-8-2009
10012750@unknown@formal@none@1@S@We may suppose this paper is divided into squares like a child's arithmetic book....I assume then that the computation is carried out on one-dimensional paper, i.e., on a tape divided into squares.@@@@1@32@@oe@19-8-2009
10012760@unknown@formal@none@1@S@I shall also suppose that the number of symbols which may be printed is finite....@@@@1@15@@oe@19-8-2009
10012770@unknown@formal@none@1@S@:"The behavior of the computer at any moment is determined by the symbols which he is observing, and his "state of mind" at that moment.@@@@1@25@@oe@19-8-2009
10012780@unknown@formal@none@1@S@We may suppose that there is a bound B to the number of symbols or squares which the computer can observe at one moment.@@@@1@24@@oe@19-8-2009
10012790@unknown@formal@none@1@S@If he wishes to observe more, he must use successive observations.@@@@1@11@@oe@19-8-2009
10012800@unknown@formal@none@1@S@We will also suppose that the number of states of mind which need be taken into account is finite...@@@@1@19@@oe@19-8-2009
10012810@unknown@formal@none@1@S@:"Let us imagine that the operations performed by the computer to be split up into 'simple operations' which are so elementary that it is not easy to imagine them further divided" (Turing 1936-7:136).@@@@1@33@@oe@19-8-2009
10012820@unknown@formal@none@1@S@Turing's reduction yields the following:@@@@1@5@@oe@19-8-2009
10012830@unknown@formal@none@1@S@:"The simple operations must therefore include:@@@@1@6@@oe@19-8-2009
10012840@unknown@formal@none@1@S@::"(a) Changes of the symbol on one of the observed squares@@@@1@11@@oe@19-8-2009
10012850@unknown@formal@none@1@S@::"(b) Changes of one of the squares observed to another square within L squares of one of the previously observed squares.@@@@1@21@@oe@19-8-2009
10012860@unknown@formal@none@1@S@"It may be that some of these change necessarily invoke a change of state of mind.@@@@1@16@@oe@19-8-2009
10012870@unknown@formal@none@1@S@The most general single operation must therefore be taken to be one of the following:@@@@1@15@@oe@19-8-2009
10012880@unknown@formal@none@1@S@::"(A) A possible change (a) of symbol together with a possible change of state of mind.@@@@1@16@@oe@19-8-2009
10012890@unknown@formal@none@1@S@::"(B) A possible change (b) of observed squares, together with a possible change of state of mind"@@@@1@17@@oe@19-8-2009
10012900@unknown@formal@none@1@S@:"We may now construct a machine to do the work of this computer."@@@@1@13@@oe@19-8-2009
10012910@unknown@formal@none@1@S@(Turing 1936-7:136)@@@@1@2@@oe@19-8-2009
10012920@unknown@formal@none@1@S@A few years later, Turing expanded his analysis (thesis, definition) with this forceful expression of it:@@@@1@16@@oe@19-8-2009
10012930@unknown@formal@none@1@S@:"A function is said to be "effectively calculable" if its values can be found by some purely mechanical process.@@@@1@19@@oe@19-8-2009
10012940@unknown@formal@none@1@S@Although it is fairly easy to get an intuitive grasp of this idea, it is neverthessless desirable to have some more definite, mathematical expressible definition . . . [he discusses the history of the definition pretty much as presented above with respect to Gödel, Herbrand, Kleene, Church, Turing and Post] . . .@@@@1@53@@oe@19-8-2009
10012950@unknown@formal@none@1@S@We may take this statement literally, understanding by a purely mechanical process one which could be carried out by a machine.@@@@1@21@@oe@19-8-2009
10012960@unknown@formal@none@1@S@It is possible to give a mathematical description, in a certain normal form, of the structures of these machines.@@@@1@19@@oe@19-8-2009
10012970@unknown@formal@none@1@S@The development of these ideas leads to the author's definition of a computable function, and to an identification of computability † with effective calculability . . . .@@@@1@28@@oe@19-8-2009
10012980@unknown@formal@none@1@S@::"† We shall use the expression "computable function" to mean a function calculable by a machine, and we let "effectively calculabile" refer to the intuitive idea without particular identification with any one of these definitions."(Turing 1939:160)@@@@1@36@@oe@19-8-2009
10012990@unknown@formal@none@1@S@=== J. B. Rosser (1939) and S. C. Kleene (1943) ===@@@@1@11@@oe@19-8-2009
10013000@unknown@formal@none@1@S@'''[[J. Barkley Rosser]]''' boldly defined an ‘effective [mathematical] method’ in the following manner (boldface added):@@@@1@15@@oe@19-8-2009
10013010@unknown@formal@none@1@S@:"'Effective method' is used here in the rather special sense of a method each step of which is precisely determined and which is certain to produce the answer in a finite number of steps.@@@@1@34@@oe@19-8-2009
10013020@unknown@formal@none@1@S@With this special meaning, three different precise definitions have been given to date. [his footnote #5; see discussion immediately below].@@@@1@20@@oe@19-8-2009
10013030@unknown@formal@none@1@S@The simplest of these to state (due to Post and Turing) says essentially that '''an effective method of solving certain sets of problems exists if one can build a machine which will then solve any problem of the set with no human intervention beyond inserting the question and (later) reading the answer'''.@@@@1@52@@oe@19-8-2009
10013040@unknown@formal@none@1@S@All three definitions are equivalent, so it doesn't matter which one is used.@@@@1@13@@oe@19-8-2009
10013050@unknown@formal@none@1@S@Moreover, the fact that all three are equivalent is a very strong argument for the correctness of any one."@@@@1@19@@oe@19-8-2009
10013060@unknown@formal@none@1@S@(Rosser 1939:225–6)@@@@1@2@@oe@19-8-2009
10013070@unknown@formal@none@1@S@Rosser's footnote #5 references the work of (1) Church and Kleene and their definition of λ-definability, in particular Church's use of it in his ''An Unsolvable Problem of Elementary Number Theory'' (1936); (2) Herbrand and Gödel and their use of recursion in particular Gödel's use in his famous paper ''On Formally Undecidable Propositions of Principia Mathematica and Related Systems I'' (1931); and (3) Post (1936) and Turing (1936-7) in their mechanism-models of computation.@@@@1@73@@oe@19-8-2009
10013080@unknown@formal@none@1@S@'''[[Stephen C. Kleene]]''' defined as his now-famous "Thesis I" known as the [[Church-Turing thesis]].@@@@1@14@@oe@19-8-2009
10013090@unknown@formal@none@1@S@But he did this in the following context (boldface in original):@@@@1@11@@oe@19-8-2009
10013100@unknown@formal@none@1@S@:"12.@@@@1@1@@oe@19-8-2009
10013110@unknown@formal@none@1@S@'''Algorithmic theories'''...@@@@1@2@@oe@19-8-2009
10013120@unknown@formal@none@1@S@In setting up a complete algorithmic theory, what we do is to describe a procedure, performable for each set of values of the independent variables, which procedure necessarily terminates and in such manner that from the outcome we can read a definite answer, "yes" or "no," to the question, "is the predicate value true?”"@@@@1@54@@oe@19-8-2009
10013130@unknown@formal@none@1@S@(Kleene 1943:273)@@@@1@2@@oe@19-8-2009
10013140@unknown@formal@none@1@S@=== History after 1950 ===@@@@1@5@@oe@19-8-2009
10013150@unknown@formal@none@1@S@A number of efforts have been directed toward further refinement of the definition of "algorithm", and activity is on-going because of issues surrounding, in particular, [[foundations of mathematics]] (especially the [[Church-Turing Thesis]]) and [[philosophy of mind]] (especially arguments around [[artificial intelligence]]).@@@@1@41@@oe@19-8-2009
10013160@unknown@formal@none@1@S@For more, see [[Algorithm characterizations]].@@@@1@5@@oe@19-8-2009
10013170@unknown@formal@none@1@S@==Algorithmic Repositories==@@@@1@2@@oe@19-8-2009
10013180@unknown@formal@none@1@S@*LEDA@@@@1@1@@oe@19-8-2009
10013190@unknown@formal@none@1@S@*Stanford GraphBase@@@@1@2@@oe@19-8-2009
10013200@unknown@formal@none@1@S@*Combinatorica@@@@1@1@@oe@19-8-2009
10013210@unknown@formal@none@1@S@*Netlib@@@@1@1@@oe@19-8-2009
10013220@unknown@formal@none@1@S@*XTango@@@@1@1@@oe@19-8-2009
10020010@unknown@formal@none@1@S@<article>Ambiguity</article>@@@@1@1@@oe@19-8-2009
10020020@unknown@formal@none@1@S@'''Ambiguity''' is the property of being '''ambiguous''', where a [[word]], term, notation, sign, [[symbol]], [[phrase]], [[Sentence (linguistics)|sentence]], or any other form used for [[communication]], is called ambiguous if it can be interpreted in more than one way.@@@@1@37@@oe@19-8-2009
10020030@unknown@formal@none@1@S@Ambiguity is distinct from ''[[vagueness]]'', which arises when the boundaries of meaning are indistinct.@@@@1@14@@oe@19-8-2009
10020040@unknown@formal@none@1@S@Ambiguity is context-dependent: the same communication may be ambiguous in one context and unambiguous in another context.@@@@1@17@@oe@19-8-2009
10020050@unknown@formal@none@1@S@For a word, ambiguity typically refers to an unclear choice between different definitions as may be found in a [[dictionary]].@@@@1@20@@oe@19-8-2009
10020060@unknown@formal@none@1@S@A sentence may be ambiguous due to different ways of [[parsing]] the same sequence of words.@@@@1@16@@oe@19-8-2009
10020070@unknown@formal@none@1@S@== Linguistic forms ==@@@@1@4@@oe@19-8-2009
10020080@unknown@formal@none@1@S@'''[[Polysemy|Lexical ambiguity]]''' arises when [[context]] is insufficient to determine the sense of a single word that has more than one meaning.@@@@1@21@@oe@19-8-2009
10020090@unknown@formal@none@1@S@For example, the word “bank” has several distinct definitions, including “financial institution” and “edge of a river,” but if someone says “I deposited $100 in the bank,” most people would not think you used a shovel to dig in the mud.@@@@1@41@@oe@19-8-2009
10020100@unknown@formal@none@1@S@The word "run" has 130 ambiguous definitions in some [[lexicon]]s.@@@@1@10@@oe@19-8-2009
10020110@unknown@formal@none@1@S@"Biweekly" can mean "fortnightly" (once every two weeks - 26 times a year), OR "twice a week" (104 times a year).@@@@1@21@@oe@19-8-2009
10020120@unknown@formal@none@1@S@Stating a specific context like "meeting schedule" does NOT disambiguate "biweekly."@@@@1@11@@oe@19-8-2009
10020130@unknown@formal@none@1@S@Many people believe that such lexically-ambiguous, miscommunication-prone words should be avoided altogether, since the user generally has to waste time, effort, and [[attention span]] to define what is meant when they are used.@@@@1@33@@oe@19-8-2009
10020140@unknown@formal@none@1@S@The use of multi-defined words requires the author or speaker to clarify their context, and sometimes elaborate on their specific intended meaning (in which case, a less ambiguous term should have been used).@@@@1@33@@oe@19-8-2009
10020150@unknown@formal@none@1@S@The goal of clear concise communication is that the receiver(s) have no misunderstanding about what was meant to be conveyed.@@@@1@20@@oe@19-8-2009
10020160@unknown@formal@none@1@S@An exception to this could include a politician whose "wiggle words" and [[obfuscation]] are necessary to gain support from multiple [[constituent (politics)]] with [[mutually exclusive]] conflicting desires from their candidate of choice.@@@@1@32@@oe@19-8-2009
10020170@unknown@formal@none@1@S@Ambiguity is a powerful tool of [[political science]].@@@@1@8@@oe@19-8-2009
10020180@unknown@formal@none@1@S@More problematic are words whose senses express closely-related concepts.@@@@1@9@@oe@19-8-2009
10020190@unknown@formal@none@1@S@“Good,” for example, can mean “useful” or “functional” (''That’s a good hammer''), “exemplary” (''She’s a good student''), “pleasing” (''This is good soup''), “moral” (''a good person'' versus ''the lesson to be learned from a story''), "[[righteous]]", etc.@@@@1@37@@oe@19-8-2009
10020200@unknown@formal@none@1@S@“I have a good daughter” is not clear about which sense is intended.@@@@1@13@@oe@19-8-2009
10020210@unknown@formal@none@1@S@The various ways to apply [[prefix]]es and [[suffix]]es can also create ambiguity (“unlockable” can mean “capable of being unlocked” or “impossible to lock”, and therefore should not be used).@@@@1@29@@oe@19-8-2009
10020220@unknown@formal@none@1@S@'''[[Syntactic ambiguity]]''' arises when a sentence can be [[parsing|parsed]] in more than one way.@@@@1@14@@oe@19-8-2009
10020230@unknown@formal@none@1@S@“He ate the cookies on the couch,” for example, could mean that he ate those cookies which were on the couch (as opposed to those that were on the table), or it could mean that he was sitting on the couch when he ate the cookies.@@@@1@46@@oe@19-8-2009
10020240@unknown@formal@none@1@S@[[Spoken language]] can contain many more types of ambiguities, where there is more than one way to compose a set of sounds into words, for example “ice cream” and “I scream.”@@@@1@31@@oe@19-8-2009
10020250@unknown@formal@none@1@S@Such ambiguity is generally resolved based on the context.@@@@1@9@@oe@19-8-2009
10020260@unknown@formal@none@1@S@A mishearing of such, based on incorrectly-resolved ambiguity, is called a [[mondegreen]].@@@@1@12@@oe@19-8-2009
10020270@unknown@formal@none@1@S@'''[[Meaning (non-linguistic)|Semantic ambiguity]]''' arises when a word or concept has an inherently diffuse meaning based on widespread or informal usage.@@@@1@20@@oe@19-8-2009
10020280@unknown@formal@none@1@S@This is often the case, for example, with idiomatic expressions whose definitions are rarely or never well-defined, and are presented in the context of a larger argument that invites a conclusion.@@@@1@31@@oe@19-8-2009
10020290@unknown@formal@none@1@S@For example, “You could do with a new automobile.@@@@1@9@@oe@19-8-2009
10020300@unknown@formal@none@1@S@How about a test drive?”@@@@1@5@@oe@19-8-2009
10020310@unknown@formal@none@1@S@The clause “You could do with” presents a statement with such wide possible interpretation as to be essentially meaningless.@@@@1@19@@oe@19-8-2009
10020320@unknown@formal@none@1@S@Lexical ambiguity is contrasted with semantic ambiguity.@@@@1@7@@oe@19-8-2009
10020330@unknown@formal@none@1@S@The former represents a choice between a finite number of known and meaningful context-dependent interpretations.@@@@1@15@@oe@19-8-2009
10020340@unknown@formal@none@1@S@The latter represents a choice between any number of possible interpretations, none of which may have a standard agreed-upon meaning.@@@@1@20@@oe@19-8-2009
10020350@unknown@formal@none@1@S@This form of ambiguity is closely related to [[vagueness]].@@@@1@9@@oe@19-8-2009
10020360@unknown@formal@none@1@S@Linguistic ambiguity can be a problem in law (see [[Ambiguity (law)]]), because the interpretation of written documents and oral agreements is often of paramount importance.@@@@1@25@@oe@19-8-2009
10020370@unknown@formal@none@1@S@==Intentional application==@@@@1@2@@oe@19-8-2009
10020380@unknown@formal@none@1@S@[[Philosopher]]s (and other users of [[logic]]) spend a lot of time and effort searching for and removing (or intentionally adding) ambiguity in arguments, because it can lead to incorrect conclusions and can be used to deliberately conceal bad arguments.@@@@1@39@@oe@19-8-2009
10020390@unknown@formal@none@1@S@For example, a politician might say “I oppose taxes that hinder economic growth.”@@@@1@13@@oe@19-8-2009
10020400@unknown@formal@none@1@S@Some will think he opposes taxes in general, because they hinder economic growth.@@@@1@13@@oe@19-8-2009
10020410@unknown@formal@none@1@S@Others may think he opposes only those taxes that he believes will hinder economic growth (although in writing, the correct insertion or omission of a [[comma (punctuation)|comma]] after “taxes” and the use of "which" can help reduce ambiguity here.@@@@1@39@@oe@19-8-2009
10020420@unknown@formal@none@1@S@For the first meaning, “, which” is properly used in place of “that”), or restructure the sentence to completely eliminate possible misinterpretation.@@@@1@22@@oe@19-8-2009
10020430@unknown@formal@none@1@S@The devious politician hopes that each [[constituent (politics)]] will interpret the above statement in the most desirable way, and think the politician supports everyone's opinion.@@@@1@25@@oe@19-8-2009
10020440@unknown@formal@none@1@S@However, the opposite can also be true - An opponent can turn a positive statement into a bad one, if the speaker uses ambiguity (intentionally or not).@@@@1@27@@oe@19-8-2009
10020450@unknown@formal@none@1@S@The logical fallacies of [[amphiboly]] and [[equivocation]] rely heavily on the use of ambiguous words and phrases.@@@@1@17@@oe@19-8-2009
10020460@unknown@formal@none@1@S@In [[literature]] and [[rhetoric]], on the other hand, ambiguity can be a useful tool.@@@@1@14@@oe@19-8-2009
10020470@unknown@formal@none@1@S@[[Groucho Marx]]’s classic joke depends on a grammatical ambiguity for its [[humor]], for example: “Last night I shot an elephant in my pajamas.@@@@1@23@@oe@19-8-2009
10020480@unknown@formal@none@1@S@What he was doing in my pajamas I’ll never know.”@@@@1@10@@oe@19-8-2009
10020490@unknown@formal@none@1@S@Ambiguity can also be used as a comic device through a genuine intention to confuse, as does Magic: The Gathering's Unhinged © Ambiguity, which makes puns with [[homophone]]s, mispunctuation, and run-ons: “Whenever a player plays a spell that counters a spell that has been played[,] or a player plays a spell that comes into play with counters, that player may counter the next spell played[,] or put an additional counter on a permanent that has already been played, but not countered.”@@@@1@81@@oe@19-8-2009
10020500@unknown@formal@none@1@S@Songs and poetry often rely on ambiguous words for artistic effect, as in the song title “Don’t It Make My Brown Eyes Blue” (where “blue” can refer to the color, or to [[sadness]]).@@@@1@33@@oe@19-8-2009
10020510@unknown@formal@none@1@S@In narrative, ambiguity can be introduced in several ways: motive, plot, character.@@@@1@12@@oe@19-8-2009
10020520@unknown@formal@none@1@S@[[F. Scott Fitzgerald]] uses the latter type of ambiguity with notable effect in his novel ''[[The Great Gatsby]]''.@@@@1@18@@oe@19-8-2009
10020530@unknown@formal@none@1@S@All [[religions]] debate the [[orthodoxy]] or [[heterodoxy]] of ambiguity.@@@@1@9@@oe@19-8-2009
10020540@unknown@formal@none@1@S@[[Christianity]] and [[Judaism]] employ the concept of [[paradox]] synonymously with 'ambiguity'.@@@@1@11@@oe@19-8-2009
10020550@unknown@formal@none@1@S@Ambiguity within Christianity (and other religions) is resisted by the conservatives and fundamentalists, who regard the concept as equating with 'contradiction'.@@@@1@21@@oe@19-8-2009
10020560@unknown@formal@none@1@S@Non-fundamentalist Christians and Jews endorse [[Rudolf Otto]]'s description of the sacred as 'mysterium tremendum et fascinans', the awe-inspiring mystery which fascinates humans.@@@@1@22@@oe@19-8-2009
10020570@unknown@formal@none@1@S@[[Metonymy]] involves the use of the name of a subcomponent part as an abbreviation, or [[jargon]], for the name of the whole object (for example "wheels" to refer to a car, or "flowers" to refer to beautiful offspring, an entire plant, or a collection of blooming plants).@@@@1@47@@oe@19-8-2009
10020580@unknown@formal@none@1@S@In modern [[vocabulary]] critical [[semiotics]], metonymy encompasses any potentially-ambiguous word substitution that is based on contextual [[contiguity]] (located close together), or a function or process that an object performs, such as "sweet ride" to refer to a nice car.@@@@1@39@@oe@19-8-2009
10020590@unknown@formal@none@1@S@Metonym miscommunication is considered a primary mechanism of linguistic humour.@@@@1@10@@oe@19-8-2009
10020600@unknown@formal@none@1@S@==Psychology and management==@@@@1@3@@oe@19-8-2009
10020610@unknown@formal@none@1@S@In sociology and social psychology, the term "ambiguity" is used to indicate situations that involve [[uncertainty]].@@@@1@16@@oe@19-8-2009
10020620@unknown@formal@none@1@S@An increasing amount of research is concentrating on how people react and respond to ambiguous situations.@@@@1@16@@oe@19-8-2009
10020630@unknown@formal@none@1@S@Much of this focuses on [[ambiguity tolerance]].@@@@1@7@@oe@19-8-2009
10020640@unknown@formal@none@1@S@A number of correlations have been found between an individual’s reaction and tolerance to ambiguity and a range of factors.@@@@1@20@@oe@19-8-2009
10020650@unknown@formal@none@1@S@Apter and Desselles (2001) for example, found a strong correlation with such attributes and factors like a greater preference for safe as opposed to risk based sports, a preference for endurance type activities as opposed to explosive activities, a more organized and less casual lifestyle, greater care and precision in descriptions, a lower sensitivity to emotional and unpleasant words, a less acute sense of humour, engaging a smaller variety of sexual practices than their more risk comfortable colleagues, a lower likelihood of the use of drugs, pornography and drink, a greater likelihood of displaying obsessional behaviour.@@@@1@96@@oe@19-8-2009
10020660@unknown@formal@none@1@S@In the field of [[leadership]] [[David Wilkinson (ambiguity expert)|David Wilkinson]] (2006) found strong correlations between an individual leaders reaction to ambiguous situations and the [[Modes of Leadership]] they use, the type of [[creativity]] (Kirton (2003) and how they relate to others.@@@@1@41@@oe@19-8-2009
10020670@unknown@formal@none@1@S@==Music==@@@@1@1@@oe@19-8-2009
10020680@unknown@formal@none@1@S@In [[music]], pieces or sections which confound expectations and may be or are interpreted simultaneously in different ways are ambiguous, such as some [[polytonality]], [[polymeter]], other ambiguous [[metre|meters]] or [[rhythm]]s, and ambiguous [[phrase (music)|phrasing]], or (Stein 2005, p.79) any [[aspect of music]].@@@@1@42@@oe@19-8-2009
10020690@unknown@formal@none@1@S@The [[music of Africa]] is often purposely ambiguous.@@@@1@8@@oe@19-8-2009
10020700@unknown@formal@none@1@S@To quote [[Donald Francis Tovey|Sir Donald Francis Tovey]] (1935, p.195), “Theorists are apt to vex themselves with vain efforts to remove uncertainty just where it has a high aesthetic value.”@@@@1@30@@oe@19-8-2009
10020710@unknown@formal@none@1@S@==Constructed language==@@@@1@2@@oe@19-8-2009
10020720@unknown@formal@none@1@S@Some [[Conlang|languages have been created]] with the intention of avoiding ambiguity, especially lexical ambiguity.@@@@1@14@@oe@19-8-2009
10020730@unknown@formal@none@1@S@[[Lojban]] and [[Loglan]] are two related languages which have been created with this in mind.@@@@1@15@@oe@19-8-2009
10020740@unknown@formal@none@1@S@The languages can be both spoken and written.@@@@1@8@@oe@19-8-2009
10020750@unknown@formal@none@1@S@These languages are intended to provide a greater technical precision over natural languages, although historically, such attempts at language improvement have been criticized.@@@@1@23@@oe@19-8-2009
10020760@unknown@formal@none@1@S@Languages composed from many diverse sources contain much ambiguity and inconsistency.@@@@1@11@@oe@19-8-2009
10020770@unknown@formal@none@1@S@The many exceptions to [[syntax]] and [[semantic]] rules are time-consuming and difficult to learn.@@@@1@14@@oe@19-8-2009
10020780@unknown@formal@none@1@S@==Mathematics and physics==@@@@1@3@@oe@19-8-2009
10020790@unknown@formal@none@1@S@[[Mathematical notation]], widely used in [[physics]] and other [[science]]s, avoids many ambiguities compared to expression in natural language.@@@@1@18@@oe@19-8-2009
10020800@unknown@formal@none@1@S@However, for various reasons, several [[Lexical (semiotics)|lexical]], [[syntactic]] and [[semantic]] ambiguities remain.@@@@1@12@@oe@19-8-2009
10020810@unknown@formal@none@1@S@===Names of functions===@@@@1@3@@oe@19-8-2009
10020820@unknown@formal@none@1@S@The <b>ambiguity<b> in the style of writing a function should not be confused with a [[multivalued function]], which can (and should) be defined in a deterministic and unambiguous way.@@@@1@29@@oe@19-8-2009
10020830@unknown@formal@none@1@S@Several [[special function]]s still do not have established notations.@@@@1@9@@oe@19-8-2009
10020840@unknown@formal@none@1@S@Usually, the conversion to another notation requires to scale the argument and/or the resulting value; sometimes, the same name of the function is used, causing confusions.@@@@1@26@@oe@19-8-2009
10020850@unknown@formal@none@1@S@Examples of such underestablished functions:@@@@1@5@@oe@19-8-2009
10020860@unknown@formal@none@1@S@* [[Sinc function]]@@@@1@3@@oe@19-8-2009
10020870@unknown@formal@none@1@S@* [[Elliptic integral#Complete_elliptic_integral_of_the_third_kind|Elliptic integral of the Third Kind]]; translating elliptic integral form [[MAPLE]] to [[Mathematica]], one should replace the second argument to its square, see [[Talk:Elliptic integral#List_of_notations]]; dealing with complex values, this may cause problems.@@@@1@35@@oe@19-8-2009
10020880@unknown@formal@none@1@S@* [[Exponential integral]], , page 228 http://www.math.sfu.ca/~cbm/aands/page_228.htm@@@@1@7@@oe@19-8-2009
10020890@unknown@formal@none@1@S@* [[Hermite polynomial]], , page 775 http://www.math.sfu.ca/~cbm/aands/page_775.htm@@@@1@7@@oe@19-8-2009
10020900@unknown@formal@none@1@S@===Expressions===@@@@1@1@@oe@19-8-2009
10020910@unknown@formal@none@1@S@Ambiguous espressions often appear in physical and mathematical texts.@@@@1@9@@oe@19-8-2009
10020920@unknown@formal@none@1@S@It is common practice to omit multiplication signs in mathematical expressions.@@@@1@11@@oe@19-8-2009
10020930@unknown@formal@none@1@S@Also, it is common, to give the same name to a variable and a function, for example, <math>~f=f(x)~</math>.@@@@1@18@@oe@19-8-2009
10020940@unknown@formal@none@1@S@Then, if one sees <math>~g=f(y+1)~</math>, there is no way to distinguish, does it mean <math>~f=f(x)~</math> '''multiplied''' by <math>~(y+1)~</math>, or function <math>~f~</math> '''evaluated''' at argument equal to <math>~(y+1)~</math>.@@@@1@27@@oe@19-8-2009
10020950@unknown@formal@none@1@S@In each case of use of such notations, the reader is supposed to be able to perform the deduction and reveal the true meaning.@@@@1@24@@oe@19-8-2009
10020960@unknown@formal@none@1@S@Creators of algorithmic languages try to avoid ambiguities.@@@@1@8@@oe@19-8-2009
10020970@unknown@formal@none@1@S@Many algorithmic languages ([[C++]], [[MATLAB]], [[Fortran]], [[Maple]]) require the character * as symbol of multiplication.@@@@1@15@@oe@19-8-2009
10020980@unknown@formal@none@1@S@The language [[Mathematica]] allows the user to omit the multiplication symbol, but requires square brackets to indicate the argument of a function; square brackets are not allowed for grouping of expressions.@@@@1@31@@oe@19-8-2009
10020990@unknown@formal@none@1@S@Fortran, in addition, does not allow use of the same name (identifier) for different objects, for example, function and variable; in particular, the expression '''f=f(x)''' is qualified as an error.@@@@1@30@@oe@19-8-2009
10021000@unknown@formal@none@1@S@The order of operations may depend on the context.@@@@1@9@@oe@19-8-2009
10021010@unknown@formal@none@1@S@In most [[programming language]]s, the operations of division and multiplication have equal priority and are executed from left to right.@@@@1@20@@oe@19-8-2009
10021020@unknown@formal@none@1@S@Until the last century, many editorials assumed that multiplication is performed first, for example, <math>~a/bc~</math> is interpreted as <math>~a/(bc)~</math>; in this case, the insertion of parentheses is required when translating the formulas to an algorithmic language.@@@@1@36@@oe@19-8-2009
10021030@unknown@formal@none@1@S@In addition, it is common to write an argument of a function without parenthesis, which also may lead to ambiguity.@@@@1@20@@oe@19-8-2009
10021040@unknown@formal@none@1@S@Sometimes, one uses ''italics'' letters to denote elementary functions.@@@@1@9@@oe@19-8-2009
10021050@unknown@formal@none@1@S@In the [[scientific journal]] style, the expression <math>~ s i n \\alpha~</math> means product of variables <math>~s~</math>, <math>~i~</math>, <math>~n~</math> and <math>~\\alpha~</math>, although in a slideshow, it may mean <math>~\\sin[\\alpha]~</math>.@@@@1@29@@oe@19-8-2009
10021060@unknown@formal@none@1@S@Comma in subscripts and superscripts sometimes is omitted; it is also ambiguous notation.@@@@1@13@@oe@19-8-2009
10021070@unknown@formal@none@1@S@If it is written <math>~T_{mnk}~</math>, the reader should guess from the context, does it mean a single-index object, evaluated while the subscript is equal to product of variables <math>~m~</math>, <math>~n~</math> and <math>~k~</math>, or it is indication to a three-valent tensor.@@@@1@40@@oe@19-8-2009
10021080@unknown@formal@none@1@S@The writing of <math>~T_{mnk}~</math> instead of <math>~T_{m,n,k}~</math> may mean that the writer either is stretched in space (for example, to reduce the publication fees, or aims to increase number of publications without considering readers.@@@@1@34@@oe@19-8-2009
10021090@unknown@formal@none@1@S@The same may apply to any other use of ambiguous notations.@@@@1@11@@oe@19-8-2009
10021100@unknown@formal@none@1@S@===Examples of potentially confusing ambiguous mathematical expressions ===@@@@1@8@@oe@19-8-2009
10021110@unknown@formal@none@1@S@<math>\\sin^2\\alpha/2\\,</math>, which could be understood to mean either <math>(\\sin(\\alpha/2))^2\\,</math> or <math>(\\sin(\\alpha))^2/2\\,</math>.@@@@1@11@@oe@19-8-2009
10021120@unknown@formal@none@1@S@<math>~\\sin^{-1} \\alpha</math>, which by convention means <math>~\\arcsin(\\alpha) ~</math>, though it might be thought to mean <math>(\\sin(\\alpha))^{-1}\\,</math> since <math>~\\sin^{n} \\alpha</math> means <math>(\\sin(\\alpha))^{n}\\,</math>.@@@@1@21@@oe@19-8-2009
10021130@unknown@formal@none@1@S@<math>a/2b\\,</math>, which arguably should mean <math>(a/2)b\\,</math> but would commonly be understood to mean <math>a/(2b)\\,</math>@@@@1@14@@oe@19-8-2009
10021140@unknown@formal@none@1@S@===Notations in [[quantum optics]] and [[quantum mechanics]]===@@@@1@7@@oe@19-8-2009
10021150@unknown@formal@none@1@S@It is common to define the [[coherent states]] in [[quantum optics]] with <math>~|\\alpha\\rangle~ </math> and states with fixed number of photons with <math>~|n\\rangle~</math>.@@@@1@23@@oe@19-8-2009
10021160@unknown@formal@none@1@S@Then, there is an "unwritten rule": the state is coherent if there are more Greek characters than Latin characters in the argument, and <math>~n~</math>photon state if the Latin characters dominate.@@@@1@30@@oe@19-8-2009
10021170@unknown@formal@none@1@S@The ambiguity becomes even worse, if <math>~|x\\rangle~</math> is used for the states with certain value of the coordinate, and <math>~|p\\rangle~</math> means the state with certain value of the momentum, which may be used in books on [[quantum mechanics]].@@@@1@38@@oe@19-8-2009
10021180@unknown@formal@none@1@S@Such ambiguities easy lead to confusions, especially if some normalized [[adimensional]], [[dimensionless]] variables are used.@@@@1@15@@oe@19-8-2009
10021190@unknown@formal@none@1@S@Expression <math> |1\\rangle </math> may mean a state with single photon, or the coherent state with mean amplitude equal to 1, or state with momentum equal to unity, and so on.@@@@1@31@@oe@19-8-2009
10021200@unknown@formal@none@1@S@The reader is supposed to guess from the context.@@@@1@9@@oe@19-8-2009
10021210@unknown@formal@none@1@S@===Examples of ambiguous terms in physics===@@@@1@6@@oe@19-8-2009
10021220@unknown@formal@none@1@S@Some physical quantities do not yet have established notations; their value (and sometimes even [[dimension]], as in the case of the [[Einstein coefficients]]) depends on the system of notations.@@@@1@29@@oe@19-8-2009
10021230@unknown@formal@none@1@S@A highly confusing term is [[gain]].@@@@1@6@@oe@19-8-2009
10021240@unknown@formal@none@1@S@For example, the sentence "the gain of a system should be doubled", without context, means close to nothing.@@@@1@18@@oe@19-8-2009
10021250@unknown@formal@none@1@S@It may mean that the ratio of the output voltage of an electric circuit to the input voltage should be doubled.@@@@1@21@@oe@19-8-2009
10021260@unknown@formal@none@1@S@It may mean that the ratio of the output power of an electric or optical circuit to the input power should be doubled.@@@@1@23@@oe@19-8-2009
10021270@unknown@formal@none@1@S@It may mean that the gain of the laser medium should be doubled, for example, doubling the population of the upper laser level in a quasi-two level system (assuming negligible absorption of the ground-state).@@@@1@34@@oe@19-8-2009
10021280@unknown@formal@none@1@S@Also, confusions may be related with the use of [[atomic percent]] as measure of concentration of a [[dopant]], or [[Optical resolution|resolution]] of an [[imaging system]], as measure of the size of the smallest detail which still can be resolved at the background of statistical noise.@@@@1@45@@oe@19-8-2009
10021290@unknown@formal@none@1@S@See also [[Accuracy and precision]] and its talk.@@@@1@8@@oe@19-8-2009
10021300@unknown@formal@none@1@S@Many terms are ambiguous.@@@@1@4@@oe@19-8-2009
10021310@unknown@formal@none@1@S@Each use of an ambiguous term should be preceded by the definition, suitable for a specific case.@@@@1@17@@oe@19-8-2009
10021320@unknown@formal@none@1@S@The [[Berry paradox]] arises as a result of systematic ambiguity.@@@@1@10@@oe@19-8-2009
10021330@unknown@formal@none@1@S@In various formulations of the Berry paradox, such as one that reads: ''The number not nameable in less than eleven syllables'' the term ''nameable'' is one that has this systematic ambiguity.@@@@1@31@@oe@19-8-2009
10021340@unknown@formal@none@1@S@Terms of this kind give rise to [[vicious circle]] fallacies.@@@@1@10@@oe@19-8-2009
10021350@unknown@formal@none@1@S@Other terms with this type of ambiguity are: satisfiable, definable, true, false, function, property, class, relation, cardinal, and ordinal.@@@@1@19@@oe@19-8-2009
10021360@unknown@formal@none@1@S@==Pedagogic use of ambiguous expressions==@@@@1@5@@oe@19-8-2009
10021370@unknown@formal@none@1@S@Ambiguity can be used as a pedagogical trick, to force students to reproduce the deduction by themselves.@@@@1@17@@oe@19-8-2009
10021380@unknown@formal@none@1@S@Some textbooks give the same name to the function and to its [[Fourier transform]]:@@@@1@14@@oe@19-8-2009
10021390@unknown@formal@none@1@S@:<math>~f(\\omega)=\\int f(t) \\exp(i\\omega t) {\\rm d}t </math>.@@@@1@7@@oe@19-8-2009
10021400@unknown@formal@none@1@S@Rigorously speaking, such an expression requires that <math>~ f=0 ~</math>; even if function <math>~ f ~</math> is a [[self-Fourier function]], the expression should be written as <math>~f(\\omega)=\\frac{1}{\\sqrt{2\\pi}}\\int f(t) \\exp(i\\omega t) {\\rm d}t </math>; however, <b>it is assumed that the shape of the function </b> (and even its norm <math>\\int |f(x)|^2 {\\rm d}x </math>) <b>depend on the character used to denote its argument<b>.@@@@1@62@@oe@19-8-2009
10021410@unknown@formal@none@1@S@If the Greek letter is used, it is assumed to be a [[Fourier transform]] of another function, The first function is assumed, if the expression in the argument contains more characters <math>~t~</math> or <math>~\\tau~</math>, than characters <math>~\\omega~</math>, and the second function is assumed in the opposite case.@@@@1@47@@oe@19-8-2009
10021420@unknown@formal@none@1@S@Expressions like <math>~f(\\omega t)~</math> or <math>~f(y)~</math> contain symbols <math>~t~</math> and <math>~\\omega~</math> in equal amounts; they are ambiguous and should be avoided in serious deduction.@@@@1@24@@oe@19-8-2009
10030010@unknown@formal@none@1@S@<article>Artificial intelligence</article>@@@@1@2@@oe@19-8-2009
10030020@unknown@formal@none@1@S@'''Artificial intelligence (AI)''' is both the [[intelligence]] of machines and the branch of [[computer science]] which aims to create it.@@@@1@20@@oe@19-8-2009
10030030@unknown@formal@none@1@S@Major AI textbooks define artificial intelligence as "the study and design of [[intelligent agents]]," where an [[intelligent agent]] is a system that perceives its environment and takes actions which maximize its chances of success.@@@@1@34@@oe@19-8-2009
10030040@unknown@formal@none@1@S@[[John McCarthy (computer scientist)|John McCarthy]], who coined the term in 1956, defines it as "the science and engineering of making intelligent machines."@@@@1@22@@oe@19-8-2009
10030050@unknown@formal@none@1@S@Among the traits that researchers hope machines will exhibit are [[:#Deduction, reasoning, problem solving|reasoning]], [[#Knowledge representation|knowledge]], [[#Planning|planning]], [[#Learning|learning]], [[#Natural language processing|communication]], [[#Perception|perception]] and the ability to [[#Motion and manipulation|move]] and manipulate objects.@@@@1@32@@oe@19-8-2009
10030055@unknown@formal@none@1@S@[[#General intelligence|General intelligence]] (or "[[strong AI]]") has not yet been achieved and is a long-term goal of some AI research.@@@@1@20@@oe@19-8-2009
10030060@unknown@formal@none@1@S@AI research uses tools and insights from many fields, including [[computer science]], [[psychology]], [[philosophy]], [[neuroscience]], [[cognitive science]], [[computational linguistics|linguistics]], [[ontology (information science)|ontology]], [[operations research]], [[computational economics|economics]], [[control theory]], [[probability]], [[optimization (mathematics)|optimization]] and [[logic]].@@@@1@33@@oe@19-8-2009
10030070@unknown@formal@none@1@S@AI research also overlaps with tasks such as [[robotics]], [[control system]]s, [[automated planning and scheduling|scheduling]], [[data mining]], [[logistics]], [[speech recognition]], [[facial recognition system|facial recognition]] and many others.@@@@1@27@@oe@19-8-2009
10030080@unknown@formal@none@1@S@Other names for the field have been proposed, such as [[computational intelligence]], [[synthetic intelligence]], [[intelligent systems]], or computational rationality.@@@@1@19@@oe@19-8-2009
10030090@unknown@formal@none@1@S@== Perspectives on AI ==@@@@1@5@@oe@19-8-2009
10030100@unknown@formal@none@1@S@=== AI in myth, fiction and speculation ===@@@@1@8@@oe@19-8-2009
10030110@unknown@formal@none@1@S@Humanity has imagined in great detail the implications of thinking machines or artificial beings.@@@@1@14@@oe@19-8-2009
10030120@unknown@formal@none@1@S@They appear in [[Greek myth]]s, such as [[Talos]] of [[Crete]], the golden robots of [[Hephaestus]] and [[Pygmalion (mythology)|Pygmalion's]] [[Galatea (mythology)|Galatea]].@@@@1@20@@oe@19-8-2009
10030130@unknown@formal@none@1@S@The earliest known humanoid robots (or [[automaton]]s) were [[cult image|sacred statue]]s worshipped in [[Egypt]] and [[Greece]], believed to have been endowed with genuine consciousness by craftsman.@@@@1@26@@oe@19-8-2009
10030140@unknown@formal@none@1@S@In the sixteenth century, the [[alchemist]] [[Paracelsus]] claimed to have created artificial beings.@@@@1@13@@oe@19-8-2009
10030150@unknown@formal@none@1@S@Realistic clockwork imitations of human beings have been built by people such as [[King Mu of Zhou#Robotics|Yan Shi]], [[Hero of Alexandria]], [[Al-Jazari]] and [[Wolfgang von Kempelen]].@@@@1@26@@oe@19-8-2009
10030160@unknown@formal@none@1@S@In modern fiction, beginning with [[Mary Shelley]]'s classic ''[[Frankenstein]],'' writers have explored the [[ethics of artificial intelligence|ethical]] issues presented by thinking machines.@@@@1@22@@oe@19-8-2009
10030170@unknown@formal@none@1@S@If a machine can be created that has intelligence, can it also ''feel''?@@@@1@13@@oe@19-8-2009
10030180@unknown@formal@none@1@S@If it can feel, does it have the same rights as a human being?@@@@1@14@@oe@19-8-2009
10030190@unknown@formal@none@1@S@This is a key issue in ''[[Frankenstein]]'' as well as in modern science fiction: for example, the film ''[[Artificial Intelligence: A.I.]]'' considers a machine in the form of a small boy which has been given the ability to feel human emotions, including, tragically, the capacity to suffer.@@@@1@47@@oe@19-8-2009
10030200@unknown@formal@none@1@S@This issue is also being considered by [[futurist]]s, such as California's [[Institute for the Future]] under the name "[[robot rights]]", although many critics believe that the discussion is premature.@@@@1@29@@oe@19-8-2009
10030210@unknown@formal@none@1@S@[[Science fiction]] writers and [[futurist]]s have also speculated on the technology's potential impact on humanity.@@@@1@15@@oe@19-8-2009
10030220@unknown@formal@none@1@S@In fiction, AI has appeared as a servant ([[R2D2]] in ''[[Star Wars]]''), a comrade ([[Data (Star Trek)|Lt. Commander Data]] in ''[[Star Trek]]''), an extension to human abilities (''[[Ghost in the Shell]]''), a conqueror (''[[The Matrix]]''), a dictator (''[[With Folded Hands]]'') and an exterminator (''[[Terminator (series)|Terminator]]'', ''[[Battlestar Galactica (re-imagining)|Battlestar Galactica]]'').@@@@1@49@@oe@19-8-2009
10030230@unknown@formal@none@1@S@Some realistic potential consequences of AI are decreased human labor demand, the enhancement of human ability or experience, and a need for redefinition of human identity and basic values.@@@@1@29@@oe@19-8-2009
10030240@unknown@formal@none@1@S@[[Futurist]]s estimate the capabilities of machines using [[Moore's Law]], which measures the relentless exponential improvement in digital technology with uncanny accuracy.@@@@1@21@@oe@19-8-2009
10030250@unknown@formal@none@1@S@[[Ray Kurzweil]] has calculated that [[desktop computer]]s will have the same processing power as human brains by the year 2029, and that by 2045 artificial intelligence will reach a point where it is able to improve ''itself'' at a rate that far exceeds anything conceivable in the past, a scenario that [[science fiction]] writer [[Vernor Vinge]] named the "[[technological singularity]]".@@@@1@60@@oe@19-8-2009
10030260@unknown@formal@none@1@S@"Artificial intelligence is the next stage in evolution," [[Edward Fredkin]] said in the 1980s, expressing an idea first proposed by [[Samuel Butler (novelist)|Samuel Butler]]'s ''[[Darwin Among the Machines]]'' (1863), and expanded upon by [[George Dyson (science historian)|George Dyson]] in his book of the same name (1998).@@@@1@46@@oe@19-8-2009
10030270@unknown@formal@none@1@S@Several [[futurist]]s and [[science fiction]] writers have predicted that human beings and machines will merge in the future into [[cyborg]]s that are more capable and powerful than either.@@@@1@28@@oe@19-8-2009
10030280@unknown@formal@none@1@S@This idea, called [[transhumanism]], has roots in [[Aldous Huxley]] and [[Robert Ettinger]], is now associated with [[robotics|robot]] designer [[Hans Moravec]], [[cybernetics|cyberneticist]] [[Kevin Warwick]] and [[Ray Kurzweil]].@@@@1@26@@oe@19-8-2009
10030290@unknown@formal@none@1@S@[[Transhumanism]] has been illustrated in fiction as well, for example on the [[manga]] ''[[Ghost in the Shell]]''@@@@1@17@@oe@19-8-2009
10030300@unknown@formal@none@1@S@=== History of AI research ===@@@@1@6@@oe@19-8-2009
10030310@unknown@formal@none@1@S@In the middle of the 20th century, a handful of scientists began a new approach to building intelligent machines, based on recent discoveries in [[neurology]], a new mathematical theory of [[information]], an understanding of control and stability called [[cybernetic]]s, and above all, by the invention of the [[digital computer]], a machine based on the abstract essence of mathematical reasoning.@@@@1@59@@oe@19-8-2009
10030320@unknown@formal@none@1@S@The field of modern AI research was founded at conference on the campus of [[Dartmouth College]] in the summer of 1956.@@@@1@21@@oe@19-8-2009
10030330@unknown@formal@none@1@S@Those who attended would become the leaders of AI research for many decades, especially [[John McCarthy (computer scientist)|John McCarthy]], [[Marvin Minsky]], [[Allen Newell]] and [[Herbert Simon]], who founded AI laboratories at [[MIT]], [[Carnegie Mellon University|CMU]] and [[Stanford]].@@@@1@37@@oe@19-8-2009
10030340@unknown@formal@none@1@S@They and their students wrote programs that were, to most people, simply astonishing: computers were solving word problems in algebra, proving logical theorems and speaking English.@@@@1@26@@oe@19-8-2009
10030350@unknown@formal@none@1@S@By the middle 60s their research was heavily funded by the [[DARPA|U.S. Department of Defense]] and they were optimistic about the future of the new field:@@@@1@26@@oe@19-8-2009
10030360@unknown@formal@none@1@S@* 1965, [[H. A. Simon]]: "[M]achines will be capable, within twenty years, of doing any work a man can do"@@@@1@20@@oe@19-8-2009
10030370@unknown@formal@none@1@S@* 1967, [[Marvin Minsky]]: "Within a generation ... the problem of creating 'artificial intelligence' will substantially be solved."@@@@1@18@@oe@19-8-2009
10030380@unknown@formal@none@1@S@These predictions, and many like them, would not come true.@@@@1@10@@oe@19-8-2009
10030390@unknown@formal@none@1@S@They had failed to recognize the difficulty of some of the problems they faced.@@@@1@14@@oe@19-8-2009
10030400@unknown@formal@none@1@S@In 1974, in response to the criticism of England's [[Sir James Lighthill]] and ongoing pressure from Congress to fund more productive projects, the U.S. and British governments cut off all undirected, exploratory research in AI.@@@@1@35@@oe@19-8-2009
10030410@unknown@formal@none@1@S@This was the first [[AI Winter]].@@@@1@6@@oe@19-8-2009
10030420@unknown@formal@none@1@S@In the early 80s, AI research was revived by the commercial success of [[expert systems]] (a form of AI program that simulated the knowledge and analytical skills of one or more human experts) and by 1985 the market for AI had reached more than a billion dollars.@@@@1@47@@oe@19-8-2009
10030430@unknown@formal@none@1@S@[[Marvin Minsky|Minsky]] and others warned the community that enthusiasm for AI had spiraled out of control and that disappointment was sure to follow.@@@@1@23@@oe@19-8-2009
10030440@unknown@formal@none@1@S@Beginning with the collapse of the [[Lisp Machine]] market in 1987, AI once again fell into disrepute, and a second, more lasting [[AI Winter]] began.@@@@1@25@@oe@19-8-2009
10030450@unknown@formal@none@1@S@In the 90s and early 21st century AI achieved its greatest successes, albeit somewhat behind the scenes.@@@@1@17@@oe@19-8-2009
10030460@unknown@formal@none@1@S@Artificial intelligence was adopted throughout the technology industry, providing the heavy lifting for [[logistics]], [[data mining]], [[medical diagnosis]] and many other areas.@@@@1@22@@oe@19-8-2009
10030470@unknown@formal@none@1@S@The success was due to several factors: the incredible power of computers today (see [[Moore's law]]), a greater emphasis on solving specific subproblems, the creation of new ties between AI and other fields working on similar problems, and above all a new commitment by researchers to solid mathematical methods and rigorous scientific standards.@@@@1@53@@oe@19-8-2009
10030480@unknown@formal@none@1@S@=== Philosophy of AI ===@@@@1@5@@oe@19-8-2009
10030490@unknown@formal@none@1@S@In a [[Computing Machinery and Intelligence|classic 1950 paper]], [[Alan Turing]] posed the question "Can Machines Think?"@@@@1@16@@oe@19-8-2009
10030500@unknown@formal@none@1@S@In the years since, the [[philosophy of artificial intelligence]] has attempted to answer it.@@@@1@14@@oe@19-8-2009
10030510@unknown@formal@none@1@S@* [[Turing Test|Turing's "polite convention"]]: ''If a machine acts as intelligently as a human being, then it is as intelligent as a human being.''@@@@1@24@@oe@19-8-2009
10030520@unknown@formal@none@1@S@[[Alan Turing]] theorized that, ultimately, we can only judge the intelligence of machine based on its behavior.@@@@1@17@@oe@19-8-2009
10030530@unknown@formal@none@1@S@This theory forms the basis of the [[Turing test]].@@@@1@9@@oe@19-8-2009
10030540@unknown@formal@none@1@S@* The [[Dartmouth Conferences|Dartmouth proposal]]: ''Every aspect of learning or any other feature of intelligence can be so precisely described that a machine can be made to simulate it.''@@@@1@29@@oe@19-8-2009
10030550@unknown@formal@none@1@S@This assertion was printed in the proposal for the [[Dartmouth Conferences|Dartmouth Conference]] of 1956, and represents the position of most working AI researchers.@@@@1@23@@oe@19-8-2009
10030560@unknown@formal@none@1@S@* [[Alan Newell|Newell]] and [[Herbert Simon|Simon]]'s physical symbol system hypothesis: ''A [[physical symbol system]] has the necessary and sufficient means of general intelligent action.''@@@@1@24@@oe@19-8-2009
10030570@unknown@formal@none@1@S@This statement claims that the essence of intelligence is symbol manipulation.@@@@1@11@@oe@19-8-2009
10030580@unknown@formal@none@1@S@[[Hubert Dreyfus]] argued that, on the contrary, human expertise depends on unconscious instinct rather than conscious symbol manipulation and on having a "feel" for the situation rather than explicit symbolic knowledge.@@@@1@31@@oe@19-8-2009
10030590@unknown@formal@none@1@S@* [[Gödel's incompleteness theorem]]: ''A [[physical symbol system]] can not prove all true statements.''@@@@1@14@@oe@19-8-2009
10030600@unknown@formal@none@1@S@[[Roger Penrose]] is among those who claim that Gödel's theorem limits what machines can do.@@@@1@15@@oe@19-8-2009
10030610@unknown@formal@none@1@S@* [[John Searle|Searle]]'s "strong AI position": ''A [[physical symbol system]] can have a [[mind]] and [[consciousness|mental states]].''@@@@1@17@@oe@19-8-2009
10030620@unknown@formal@none@1@S@Searle counters this assertion with his [[Chinese room]] argument, which asks us to look ''inside'' the computer and try to find where the "mind" might be.@@@@1@26@@oe@19-8-2009
10030630@unknown@formal@none@1@S@* The [[artificial brain]] argument: ''The brain can be simulated.''@@@@1@10@@oe@19-8-2009
10030640@unknown@formal@none@1@S@[[Hans Moravec]], [[Ray Kurzweil]] and others have argued that it is technologically feasible to copy the brain directly into hardware and software, and that such a simulation will be essentially identical to the original.@@@@1@34@@oe@19-8-2009
10030650@unknown@formal@none@1@S@This argument combines the idea that a [[Turing complete|suitably powerful]] machine can simulate any process, with the [[materialist]] idea that the [[mind]] is the result of a physical process in the [[brain]].@@@@1@32@@oe@19-8-2009
10030660@unknown@formal@none@1@S@== AI research ==@@@@1@4@@oe@19-8-2009
10030670@unknown@formal@none@1@S@=== Problems of AI ===@@@@1@5@@oe@19-8-2009
10030680@unknown@formal@none@1@S@While there is no universally accepted definition of intelligence, AI researchers have studied several traits that are considered essential.@@@@1@19@@oe@19-8-2009
10030690@unknown@formal@none@1@S@====Deduction, reasoning, problem solving ====@@@@1@5@@oe@19-8-2009
10030700@unknown@formal@none@1@S@Early AI researchers developed algorithms that imitated the process of conscious, step-by-step reasoning that human beings use when they solve puzzles, play board games, or make logical deductions.@@@@1@28@@oe@19-8-2009
10030710@unknown@formal@none@1@S@By the late 80s and 90s, AI research had also developed highly successful methods for dealing with [[uncertainty|uncertain]] or incomplete information, employing concepts from [[probability]] and [[economics]].@@@@1@27@@oe@19-8-2009
10030720@unknown@formal@none@1@S@For difficult problems, most of these algorithms can require enormous computational resources — most experience a "[[combinatorial explosion]]": the amount of memory or computer time required becomes astronomical when the problem goes beyond a certain size.@@@@1@36@@oe@19-8-2009
10030730@unknown@formal@none@1@S@The search for more efficient problem solving algorithms is a high priority for AI research.@@@@1@15@@oe@19-8-2009
10030740@unknown@formal@none@1@S@It is not clear, however, that conscious human reasoning is any more efficient when faced with a difficult abstract problem.@@@@1@20@@oe@19-8-2009
10030750@unknown@formal@none@1@S@[[Cognitive science|Cognitive scientists]] have demonstrated that human beings solve most of their problems using [[unconscious]] reasoning, rather than the conscious, step-by-step deduction that early AI research was able to model.@@@@1@30@@oe@19-8-2009
10030760@unknown@formal@none@1@S@[[Embodied cognitive science]] argues that unconscious [[sensorimotor]] skills are essential to our problem solving abilities.@@@@1@15@@oe@19-8-2009
10030770@unknown@formal@none@1@S@It is hoped that sub-symbolic methods, like [[computational intelligence]] and [[situated]] AI, will be able to model these instinctive skills.@@@@1@20@@oe@19-8-2009
10030780@unknown@formal@none@1@S@The problem of unconscious problem solving, which forms part of our [[commonsense reasoning]], is largely unsolved.@@@@1@16@@oe@19-8-2009
10030790@unknown@formal@none@1@S@====Knowledge representation====@@@@1@2@@oe@19-8-2009
10030800@unknown@formal@none@1@S@[[Knowledge representation]] and [[knowledge engineering]] are central to AI research.@@@@1@10@@oe@19-8-2009
10030810@unknown@formal@none@1@S@Many of the problems machines are expected to solve will require extensive knowledge about the world.@@@@1@16@@oe@19-8-2009
10030820@unknown@formal@none@1@S@Among the things that AI needs to represent are: objects, properties, categories and relations between objects; situations, events, states and time; causes and effects; knowledge about knowledge (what we know about what other people know); and many other, less well researched domains.@@@@1@42@@oe@19-8-2009
10030830@unknown@formal@none@1@S@A complete representation of "what exists" is an [[ontology (computer science)|ontology]] (borrowing a word from traditional [[philosophy]]), of which the most general are called [[upper ontology|upper ontologies]].@@@@1@27@@oe@19-8-2009
10030840@unknown@formal@none@1@S@Among the most difficult problems in knowledge representation are:@@@@1@9@@oe@19-8-2009
10030850@unknown@formal@none@1@S@* ''Default reasoning and the [[qualification problem]]'': Many of the things people know take the form of "working assumptions."@@@@1@19@@oe@19-8-2009
10030860@unknown@formal@none@1@S@For example, if a bird comes up in conversation, people typically picture an animal that is fist sized, sings, and flies.@@@@1@21@@oe@19-8-2009
10030870@unknown@formal@none@1@S@None of these things are true about birds in general.@@@@1@10@@oe@19-8-2009
10030880@unknown@formal@none@1@S@[[John McCarthy (computer scientist)|John McCarthy]] identified this problem in 1969 as the qualification problem: for any commonsense rule that AI researchers care to represent, there tend to be a huge number of exceptions.@@@@1@33@@oe@19-8-2009
10030890@unknown@formal@none@1@S@Almost nothing is simply true or false in the way that abstract logic requires.@@@@1@14@@oe@19-8-2009
10030900@unknown@formal@none@1@S@AI research has explored a number of solutions to this problem.@@@@1@11@@oe@19-8-2009
10030910@unknown@formal@none@1@S@* ''Unconscious knowledge'': Much of what people know isn't represented as "facts" or "statements" that they could actually say out loud.@@@@1@21@@oe@19-8-2009
10030920@unknown@formal@none@1@S@They take the form of intuitions or tendencies and are represented in the brain unconsciously and sub-symbolically.@@@@1@17@@oe@19-8-2009
10030930@unknown@formal@none@1@S@This unconscious knowledge informs, supports and provides a context for our conscious knowledge.@@@@1@13@@oe@19-8-2009
10030940@unknown@formal@none@1@S@As with the related problem of unconscious reasoning, it is hoped that [[situated]] AI or [[computational intelligence]] will provide ways to represent this kind of knowledge.@@@@1@26@@oe@19-8-2009
10030950@unknown@formal@none@1@S@* ''The breadth of [[common sense knowledge]]'': The number of atomic facts that the average person knows is astronomical.@@@@1@19@@oe@19-8-2009
10030960@unknown@formal@none@1@S@Research projects that attempt to build a complete knowledge base of [[commonsense knowledge]], such as [[Cyc]], require enormous amounts of tedious step-by-step ontological engineering — they must be built, by hand, one complicated concept at a time.@@@@1@37@@oe@19-8-2009
10030970@unknown@formal@none@1@S@====Planning====@@@@1@1@@oe@19-8-2009
10030980@unknown@formal@none@1@S@Intelligent agents must be able to set goals and achieve them.@@@@1@11@@oe@19-8-2009
10030990@unknown@formal@none@1@S@They need a way to visualize the future: they must have a representation of the state of the world and be able to make predictions about how their actions will change it.@@@@1@32@@oe@19-8-2009
10031000@unknown@formal@none@1@S@They must also attempt to determine the [[utility]] or "value" of the choices available to it.@@@@1@16@@oe@19-8-2009
10031010@unknown@formal@none@1@S@In some planning problems, the agent can assume that it is the only thing acting on the world and it can be certain what the consequences of its actions may be.@@@@1@31@@oe@19-8-2009
10031020@unknown@formal@none@1@S@However, if this is not true, it must periodically check if the world matches its predictions and it must change its plan as this becomes necessary, requiring the agent to reason under uncertainty.@@@@1@33@@oe@19-8-2009
10031030@unknown@formal@none@1@S@[[Multi-agent planning]] tries to determine the best plan for a community of [[agent]]s, using [[cooperation]] and [[competition]] to achieve a given goal.@@@@1@22@@oe@19-8-2009
10031040@unknown@formal@none@1@S@[[Emergent behavior]] such as this is used by both [[evolutionary algorithm]]s and [[swarm intelligence]].@@@@1@14@@oe@19-8-2009
10031050@unknown@formal@none@1@S@====Learning====@@@@1@1@@oe@19-8-2009
10031060@unknown@formal@none@1@S@Important [[machine learning]] problems are:@@@@1@5@@oe@19-8-2009
10031070@unknown@formal@none@1@S@* [[Unsupervised learning]]: find a model that matches a stream of input "experiences", and be able to predict what new "experiences" to expect.@@@@1@23@@oe@19-8-2009
10031080@unknown@formal@none@1@S@* [[Supervised learning]], such as [[statistical classification|classification]] (be able to determine what category something belongs in, after seeing a number of examples of things from each category), or [[regression]] (given a set of numerical input/output examples, discover a continuous function that would generate the outputs from the inputs).@@@@1@48@@oe@19-8-2009
10031090@unknown@formal@none@1@S@* [[Reinforcement learning]]: the agent is rewarded for good responses and punished for bad ones.@@@@1@15@@oe@19-8-2009
10031100@unknown@formal@none@1@S@(These can be analyzed in terms [[decision theory]], using concepts like [[utility (economics)|utility]]).@@@@1@13@@oe@19-8-2009
10031110@unknown@formal@none@1@S@====Natural language processing====@@@@1@3@@oe@19-8-2009
10031120@unknown@formal@none@1@S@[[Natural language processing]] gives machines the ability to read and understand the languages human beings speak.@@@@1@16@@oe@19-8-2009
10031130@unknown@formal@none@1@S@Many researchers hope that a sufficiently powerful natural language processing system would be able to acquire knowledge on its own, by reading the existing text available over the internet.@@@@1@29@@oe@19-8-2009
10031140@unknown@formal@none@1@S@Some straightforward applications of natural language processing include [[information retrieval]] (or [[text mining]]) and [[machine translation]].@@@@1@16@@oe@19-8-2009
10031150@unknown@formal@none@1@S@====Motion and manipulation====@@@@1@3@@oe@19-8-2009
10031160@unknown@formal@none@1@S@The field of [[robotics]] is closely related to AI.@@@@1@9@@oe@19-8-2009
10031170@unknown@formal@none@1@S@Intelligence is required for robots to be able to handle such tasks as object manipulation and [[motion planning|navigation]], with sub-problems of [[localization]] (knowing where you are), [[robotic mapping|mapping]] (learning what is around you) and [[motion planning]] (figuring out how to get there).@@@@1@42@@oe@19-8-2009
10031180@unknown@formal@none@1@S@====Perception====@@@@1@1@@oe@19-8-2009
10031190@unknown@formal@none@1@S@[[Machine perception]] is the ability to use input from sensors (such as cameras, microphones, sonar and others more exotic) to deduce aspects of the world.@@@@1@25@@oe@19-8-2009
10031200@unknown@formal@none@1@S@[[Computer vision]] is the ability to analyze visual input.@@@@1@9@@oe@19-8-2009
10031210@unknown@formal@none@1@S@A few selected subproblems are [[speech recognition]], [[facial recognition]] and [[object recognition]].@@@@1@12@@oe@19-8-2009
10031220@unknown@formal@none@1@S@====Social intelligence====@@@@1@2@@oe@19-8-2009
10031230@unknown@formal@none@1@S@Emotion and social skills play two roles for an intelligent agent:@@@@1@11@@oe@19-8-2009
10031240@unknown@formal@none@1@S@* It must be able to predict the actions of others, by understanding their motives and emotional states.@@@@1@18@@oe@19-8-2009
10031250@unknown@formal@none@1@S@(This involves elements of [[game theory]], [[decision theory]], as well as the ability to model human emotions and the perceptual skills to detect emotions.)@@@@1@24@@oe@19-8-2009
10031260@unknown@formal@none@1@S@* For good [[human-computer interaction]], an intelligent machine also needs to ''display'' emotions — at the very least it must appear polite and sensitive to the humans it interacts with.@@@@1@30@@oe@19-8-2009
10031270@unknown@formal@none@1@S@At best, it should appear to have normal emotions itself.@@@@1@10@@oe@19-8-2009
10031280@unknown@formal@none@1@S@====Creativity====@@@@1@1@@oe@19-8-2009
10031290@unknown@formal@none@1@S@A sub-field of AI addresses [[creativity]] both theoretically (from a philosophical and psychological perspective) and practically (via specific implementations of systems that generate outputs that can be considered creative).@@@@1@29@@oe@19-8-2009
10031300@unknown@formal@none@1@S@====General intelligence====@@@@1@2@@oe@19-8-2009
10031310@unknown@formal@none@1@S@Most researchers hope that their work will eventually be incorporated into a machine with ''general'' intelligence (known as [[strong AI]]), combining all the skills above and exceeding human abilities at most or all of them.@@@@1@35@@oe@19-8-2009
10031320@unknown@formal@none@1@S@A few believe that [[anthropomorphic]] features like [[artificial consciousness]] or an [[artificial brain]] may be required for such a project.@@@@1@20@@oe@19-8-2009
10031330@unknown@formal@none@1@S@Many of the problems above are considered [[AI-complete]]: to solve one problem, you must solve them all.@@@@1@17@@oe@19-8-2009
10031340@unknown@formal@none@1@S@For example, even a straightforward, specific task like [[machine translation]] requires that the machine follow the author's argument ([[#Deduction, reasoning, problem solving|reason]]), know what it's talking about ([[#Knowledge representation|knowledge]]), and faithfully reproduce the author's intention ([[#Social intelligence|social intelligence]]).@@@@1@38@@oe@19-8-2009
10031350@unknown@formal@none@1@S@[[Machine translation]], therefore, is believed to be AI-complete: it may require [[strong AI]] to be done as well as humans can do it.@@@@1@23@@oe@19-8-2009
10031360@unknown@formal@none@1@S@=== Approaches to AI ===@@@@1@5@@oe@19-8-2009
10031370@unknown@formal@none@1@S@There are as many approaches to AI as there are AI researchers—any coarse categorization is likely to be unfair to someone.@@@@1@21@@oe@19-8-2009
10031380@unknown@formal@none@1@S@Artificial intelligence communities have grown up around particular problems, institutions and researchers, as well as the theoretical insights that define the approaches described below.@@@@1@24@@oe@19-8-2009
10031390@unknown@formal@none@1@S@Artificial intelligence is a young science and is still a fragmented collection of subfields.@@@@1@14@@oe@19-8-2009
10031400@unknown@formal@none@1@S@At present, there is no established unifying theory that links the subfields into a coherent whole.@@@@1@16@@oe@19-8-2009
10031410@unknown@formal@none@1@S@==== Cybernetics and brain simulation ====@@@@1@6@@oe@19-8-2009
10031420@unknown@formal@none@1@S@In the 40s and 50s, a number of researchers explored the connection between [[neurology]], [[information theory]], and [[cybernetics]].@@@@1@18@@oe@19-8-2009
10031430@unknown@formal@none@1@S@Some of them built machines that used electronic networks to exhibit rudimentary intelligence, such as [[W. Grey Walter]]'s [[Turtle (robot)|turtles]] and the [[Johns Hopkins Beast]].@@@@1@25@@oe@19-8-2009
10031440@unknown@formal@none@1@S@Many of these researchers gathered for meetings of the [[Teleological Society]] at Princeton and the [[Ratio Club]] in England.@@@@1@19@@oe@19-8-2009
10031450@unknown@formal@none@1@S@==== Traditional symbolic AI ====@@@@1@5@@oe@19-8-2009
10031460@unknown@formal@none@1@S@When access to digital computers became possible in the middle 1950s, AI research began to explore the possibility that human intelligence could be reduced to symbol manipulation.@@@@1@27@@oe@19-8-2009
10031470@unknown@formal@none@1@S@The research was centered in three institutions: [[Carnegie Mellon University|CMU]], [[Stanford]] and [[MIT]], and each one developed its own style of research.@@@@1@22@@oe@19-8-2009
10031480@unknown@formal@none@1@S@[[John Haugeland]] named these approaches to AI "good old fashioned AI" or "[[GOFAI]]".@@@@1@13@@oe@19-8-2009
10031490@unknown@formal@none@1@S@; Cognitive simulation:@@@@1@3@@oe@19-8-2009
10031495@unknown@formal@none@1@S@[[Economist]] [[Herbert Simon]] and [[Alan Newell]] studied human problem solving skills and attempted to formalize them, and their work laid the foundations of the field of artificial intelligence, as well as [[cognitive science]], [[operations research]] and [[management science]].@@@@1@38@@oe@19-8-2009
10031500@unknown@formal@none@1@S@Their research team performed [[psychology|psychological]] experiments to demonstrate the similarities between human problem solving and the programs (such as their "[[General Problem Solver]]") they were developing.@@@@1@26@@oe@19-8-2009
10031510@unknown@formal@none@1@S@This tradition, centered at [[Carnegie Mellon University]], would eventually culminate in the development of the [[Soar (cognitive architecture)|Soar]] architecture in the middle 80s.@@@@1@23@@oe@19-8-2009
10031520@unknown@formal@none@1@S@; Logical AI:@@@@1@3@@oe@19-8-2009
10031525@unknown@formal@none@1@S@Unlike [[Alan Newell|Newell]] and [[Herbert Simon|Simon]], [[John McCarthy (computer scientist)|John McCarthy]] felt that machines did not need to simulate human thought, but should instead try to find the essence of abstract reasoning and problem solving, regardless of whether people used the same algorithms.@@@@1@43@@oe@19-8-2009
10031530@unknown@formal@none@1@S@His laboratory at [[Stanford University|Stanford]] ([[Stanford Artificial Intelligence Laboratory|SAIL]]) focused on using formal [[logic]] to solve a wide variety of problems, including [[knowledge representation]], [[automated planning and scheduling|planning]] and [[machine learning|learning]].@@@@1@31@@oe@19-8-2009
10031540@unknown@formal@none@1@S@Work in logic led to the development of the programming language [[Prolog]] and the science of [[logic programming]].@@@@1@18@@oe@19-8-2009
10031550@unknown@formal@none@1@S@; "Scruffy" symbolic AI:@@@@1@4@@oe@19-8-2009
10031555@unknown@formal@none@1@S@Researchers at [[MIT]] (such as [[Marvin Minsky]] and [[Seymour Papert]]) found that solving difficult problems in [[computer vision|vision]] and [[natural language processing]] required ad-hoc solutions &ndash; they argued that there was no [[silver bullet|easy answer]], no simple and general principle (like [[logic]]) that would capture all the aspects of intelligent behavior.@@@@1@51@@oe@19-8-2009
10031560@unknown@formal@none@1@S@[[Roger Schank]] described their "anti-logic" approaches as "[[Neats vs. scruffies|scruffy]]" (as opposed to the "[[Neats vs. scruffies|neat]]" paradigms at [[CMU]] and [[Stanford]]), and this still forms the basis of research into [[commonsense knowledge bases]] (such as [[Doug Lenat]]'s [[Cyc]]) which must be built one complicated concept at a time.@@@@1@49@@oe@19-8-2009
10031570@unknown@formal@none@1@S@; Knowledge based AI:@@@@1@4@@oe@19-8-2009
10031575@unknown@formal@none@1@S@When computers with large memories became available around 1970, researchers from all three traditions began to build [[knowledge representation|knowledge]] into AI applications.@@@@1@22@@oe@19-8-2009
10031580@unknown@formal@none@1@S@This "knowledge revolution" led to the development and deployment of [[expert system]]s (introduced by [[Edward Feigenbaum]]), the first truly successful form of AI software.@@@@1@24@@oe@19-8-2009
10031590@unknown@formal@none@1@S@The knowledge revolution was also driven by the realization that truly enormous amounts of knowledge would be required by many simple AI applications.@@@@1@23@@oe@19-8-2009
10031600@unknown@formal@none@1@S@==== Sub-symbolic AI ====@@@@1@4@@oe@19-8-2009
10031610@unknown@formal@none@1@S@During the 1960s, symbolic approaches had achieved great success at simulating high-level thinking in small demonstration programs.@@@@1@17@@oe@19-8-2009
10031620@unknown@formal@none@1@S@Approaches based on [[cybernetics]] or [[neural network]]s were abandoned or pushed into the background.@@@@1@14@@oe@19-8-2009
10031630@unknown@formal@none@1@S@By the 1980s, however, progress in symbolic AI seemed to stall and many believed that symbolic systems would never be able to imitate all the processes of human cognition, especially [[machine perception|perception]], [[robotics]], [[machine learning|learning]] and [[pattern recognition]].@@@@1@38@@oe@19-8-2009
10031640@unknown@formal@none@1@S@A number of researchers began to look into "sub-symbolic" approaches to specific AI problems.@@@@1@14@@oe@19-8-2009
10031650@unknown@formal@none@1@S@; Bottom-up, situated, behavior based or nouvelle AI:@@@@1@8@@oe@19-8-2009
10031655@unknown@formal@none@1@S@Researchers from the related field of [[robotics]], such as [[Rodney Brooks]], rejected symbolic AI and focussed on the basic engineering problems that would allow robots to move and survive.@@@@1@29@@oe@19-8-2009
10031660@unknown@formal@none@1@S@Their work revived the non-symbolic viewpoint of the early [[cybernetic]]s researchers of the 50s and reintroduced the use of [[control theory]] in AI.@@@@1@23@@oe@19-8-2009
10031670@unknown@formal@none@1@S@These approaches are also conceptually related to the [[embodied mind thesis]].@@@@1@11@@oe@19-8-2009
10031680@unknown@formal@none@1@S@; Computational Intelligence:@@@@1@3@@oe@19-8-2009
10031685@unknown@formal@none@1@S@Interest in [[neural networks]] and "[[connectionism]]" was revived by [[David Rumelhart]] and others in the middle 1980s.@@@@1@17@@oe@19-8-2009
10031690@unknown@formal@none@1@S@These and other sub-symbolic approaches, such as [[fuzzy system]]s and [[evolutionary computation]], are now studied collectively by the emerging discipline of [[computational intelligence]].@@@@1@23@@oe@19-8-2009
10031700@unknown@formal@none@1@S@; The new neats:@@@@1@4@@oe@19-8-2009
10031705@unknown@formal@none@1@S@In the 1990s, AI researchers developed sophisticated mathematical tools to solve specific subproblems.@@@@1@13@@oe@19-8-2009
10031710@unknown@formal@none@1@S@These tools are truly [[scientific method|scientific]], in the sense that their results are both measurable and verifiable, and they have been responsible for many of AI's recent successes.@@@@1@28@@oe@19-8-2009
10031720@unknown@formal@none@1@S@The shared mathematical language has also permitted a high level of collaboration with more established fields (like [[mathematics]], [[economics]] or [[operations research]]).@@@@1@22@@oe@19-8-2009
10031725@unknown@formal@none@1@S@{{Harvtxt|Russell|Norvig|2003}} describe this movement as nothing less than a "revolution" and "the victory of the [[neats and scruffies|neats]]."@@@@1@18@@oe@19-8-2009
10031730@unknown@formal@none@1@S@==== Intelligent agent paradigm ====@@@@1@5@@oe@19-8-2009
10031740@unknown@formal@none@1@S@The "[[intelligent agent]]" [[paradigm]] became widely accepted during the 1990s.@@@@1@10@@oe@19-8-2009
10031750@unknown@formal@none@1@S@An [[intelligent agent]] is a system that perceives its [[agent environment|environment]] and takes actions which maximizes its chances of success.@@@@1@20@@oe@19-8-2009
10031760@unknown@formal@none@1@S@The simplest intelligent agents are programs that solve specific problems.@@@@1@10@@oe@19-8-2009
10031770@unknown@formal@none@1@S@The most complicated intelligent agents are rational, thinking human beings.@@@@1@10@@oe@19-8-2009
10031780@unknown@formal@none@1@S@The paradigm gives researchers license to study isolated problems and find solutions that are both verifiable and useful, without agreeing on one single approach.@@@@1@24@@oe@19-8-2009
10031790@unknown@formal@none@1@S@An agent that solves a specific problem can use any approach that works — some agents are symbolic and logical, some are sub-symbolic [[neural network]]s and others may use new approaches.@@@@1@31@@oe@19-8-2009
10031800@unknown@formal@none@1@S@The paradigm also gives researchers a common language to communicate with other fields—such as [[decision theory]] and [[economics]]—that also use concepts of abstract agents.@@@@1@24@@oe@19-8-2009
10031810@unknown@formal@none@1@S@==== Integrating the approaches ====@@@@1@5@@oe@19-8-2009
10031820@unknown@formal@none@1@S@An [[agent architecture]] or [[cognitive architecture]] allows researchers to build more versatile and intelligent systems out of interacting [[intelligent agents]] in a [[multi-agent system]].@@@@1@24@@oe@19-8-2009
10031830@unknown@formal@none@1@S@A system with both symbolic and sub-symbolic components is a [[hybrid intelligent system]], and the study of such systems is [[artificial intelligence systems integration]].@@@@1@24@@oe@19-8-2009
10031840@unknown@formal@none@1@S@A [[hierarchical control system]] provides a bridge between sub-symbolic AI at its lowest, reactive levels and traditional symbolic AI at its highest levels, where relaxed time constraints permit planning and world modelling.@@@@1@32@@oe@19-8-2009
10031850@unknown@formal@none@1@S@[[Rodney Brooks]]' [[subsumption architecture]] was an early proposal for such a hierarchical system.@@@@1@13@@oe@19-8-2009
10031860@unknown@formal@none@1@S@=== Tools of AI research ===@@@@1@6@@oe@19-8-2009
10031870@unknown@formal@none@1@S@In the course of 50 years of research, AI has developed a large number of tools to solve the most difficult problems in [[computer science]].@@@@1@25@@oe@19-8-2009
10031880@unknown@formal@none@1@S@A few of the most general of these methods are discussed below.@@@@1@12@@oe@19-8-2009
10031890@unknown@formal@none@1@S@==== Search ====@@@@1@3@@oe@19-8-2009
10031900@unknown@formal@none@1@S@Many problems in AI can be solved in theory by intelligently searching through many possible solutions: [[:#Deduction, reasoning, problem solving|Reasoning]] can be reduced to performing a search.@@@@1@27@@oe@19-8-2009
10031910@unknown@formal@none@1@S@For example, logical proof can be viewed as searching for a path that leads from [[premise]]s to [[conclusion]]s, where each step is the application of an [[inference rule]].@@@@1@28@@oe@19-8-2009
10031920@unknown@formal@none@1@S@[[Automated planning and scheduling|Planning]] algorithms search through trees of goals and subgoals, attempting to find a path to a target goal.@@@@1@21@@oe@19-8-2009
10031930@unknown@formal@none@1@S@[[Robotics]] algorithms for moving limbs and grasping objects use [[local search (optimization)|local searches]] in [[configuration space]].@@@@1@16@@oe@19-8-2009
10031940@unknown@formal@none@1@S@Many [[machine learning|learning]] algorithms have search at their core.@@@@1@9@@oe@19-8-2009
10031950@unknown@formal@none@1@S@There are several types of search algorithms:@@@@1@7@@oe@19-8-2009
10031960@unknown@formal@none@1@S@* "Uninformed" search algorithms eventually search through every possible answer until they locate their goal.@@@@1@15@@oe@19-8-2009
10031970@unknown@formal@none@1@S@Naive algorithms quickly run into problems when they expand the size of their [[search space]] to [[astronomical]] numbers.@@@@1@18@@oe@19-8-2009
10031980@unknown@formal@none@1@S@The result is a search that is [[Computation time|too slow]] or never completes.@@@@1@13@@oe@19-8-2009
10031990@unknown@formal@none@1@S@* [[Heuristic]] or "informed" searches use heuristic methods to eliminate choices that are unlikely to lead to their goal, thus drastically reducing the number of possibilities they must explore.@@@@1@29@@oe@19-8-2009
10032000@unknown@formal@none@1@S@The eliminatation of choices that are certain not to lead to the goal is called [[pruning (algorithm)|pruning]].@@@@1@17@@oe@19-8-2009
10032010@unknown@formal@none@1@S@* [[Local search (optimization)|Local searches]], such as [[hill climbing]], [[simulated annealing]] and [[beam search]], use techniques borrowed from [[optimization (mathematics)|optimization theory]].@@@@1@21@@oe@19-8-2009
10032020@unknown@formal@none@1@S@* [[Global optimization|Global searches]] are more robust in the presence of [[local optima]].@@@@1@13@@oe@19-8-2009
10032030@unknown@formal@none@1@S@Techniques include [[evolutionary algorithms]], [[swarm intelligence]] and [[random optimization]] algorithms.@@@@1@10@@oe@19-8-2009
10032040@unknown@formal@none@1@S@==== Logic ====@@@@1@3@@oe@19-8-2009
10032050@unknown@formal@none@1@S@[[Logic]] was introduced into AI research by [[John McCarthy (computer scientist)|John McCarthy]] in his 1958 [[Advice Taker]] proposal.@@@@1@18@@oe@19-8-2009
10032060@unknown@formal@none@1@S@The most important technical development was [[J. Alan Robinson]]'s discovery of the [[resolution (logic)|resolution]] and [[unification]] algorithm for logical deduction in 1963.@@@@1@22@@oe@19-8-2009
10032070@unknown@formal@none@1@S@This procedure is simple, complete and entirely algorithmic, and can easily be performed by digital computers.@@@@1@16@@oe@19-8-2009
10032080@unknown@formal@none@1@S@However, a naive implementation of the algorithm quickly leads to a [[combinatorial explosion]] or an [[infinite loop]].@@@@1@17@@oe@19-8-2009
10032090@unknown@formal@none@1@S@In 1974, [[Robert Kowalski]] suggested representing logical expressions as [[Horn clauses]] (statements in the form of rules: "if ''p'' then ''q''"), which reduced logical deduction to [[backward chaining]] or [[forward chaining]].@@@@1@31@@oe@19-8-2009
10032100@unknown@formal@none@1@S@This greatly alleviated (but did not eliminate) the problem.@@@@1@9@@oe@19-8-2009
10032110@unknown@formal@none@1@S@Logic is used for knowledge representation and problem solving, but it can be applied to other problems as well.@@@@1@19@@oe@19-8-2009
10032120@unknown@formal@none@1@S@For example, the [[satplan]] algorithm uses logic for [[automated planning and scheduling|planning]], and [[inductive logic programming]] is a method for [[machine learning|learning]].@@@@1@22@@oe@19-8-2009
10032130@unknown@formal@none@1@S@There are several different forms of logic used in AI research.@@@@1@11@@oe@19-8-2009
10032140@unknown@formal@none@1@S@* [[Propositional logic]] or [[sentential logic]] is the logic of statements which can be true or false.@@@@1@17@@oe@19-8-2009
10032150@unknown@formal@none@1@S@* [[First-order logic]] also allows the use of [[quantifier]]s and [[predicate]]s, and can express facts about objects, their properties, and their relations with each other.@@@@1@25@@oe@19-8-2009
10032160@unknown@formal@none@1@S@* [[Fuzzy logic]], a version of first-order logic which allows the truth of a statement to be represented as a value between 0 and 1, rather than simply True (1) or False (0).@@@@1@33@@oe@19-8-2009
10032170@unknown@formal@none@1@S@[[Fuzzy system]]s can be used for uncertain reasoning and have been widely used in modern industrial and consumer product control systems.@@@@1@21@@oe@19-8-2009
10032180@unknown@formal@none@1@S@* [[Default logic]]s, [[non-monotonic logic]]s and [[circumscription]] are forms of logic designed to help with default reasoning and the [[qualification problem]].@@@@1@21@@oe@19-8-2009
10032190@unknown@formal@none@1@S@* Several extensions of logic have been designed to handle specific domains of [[knowledge representation|knowledge]], such as: [[description logic]]s; [[situation calculus]], [[event calculus]] and [[fluent calculus]] (for representing events and time); [[Causality#causal calculus|causal calculus]]; [[belief calculus]]; and [[modal logic]]s.@@@@1@39@@oe@19-8-2009
10032200@unknown@formal@none@1@S@====Probabilistic methods for uncertain reasoning====@@@@1@5@@oe@19-8-2009
10032210@unknown@formal@none@1@S@Many problems in AI (in reasoning, planning, learning, perception and robotics) require the agent to operate with incomplete or uncertain information.@@@@1@21@@oe@19-8-2009
10032220@unknown@formal@none@1@S@Starting in the late 80s and early 90s, [[Judea Pearl]] and others championed the use of methods drawn from [[probability]] theory and [[economics]] to devise a number of powerful tools to solve these problems.@@@@1@34@@oe@19-8-2009
10032230@unknown@formal@none@1@S@[[Bayesian network]]s are very general tool that can be used for a large number of problems: reasoning (using the [[Bayesian inference]] algorithm), [[Machine learning|learning]] (using the [[expectation-maximization algorithm]]), [[Automated planning and scheduling|planning]] (using [[decision network]]s) and [[machine perception|perception]] (using [[dynamic Bayesian network]]s).@@@@1@42@@oe@19-8-2009
10032240@unknown@formal@none@1@S@Probabilistic algorithms can also be used for filtering, prediction, smoothing and finding explanations for streams of data, helping [[machine perception|perception]] systems to analyze processes that occur over time (e.g., [[hidden Markov model]]s and [[Kalman filter]]s).@@@@1@35@@oe@19-8-2009
10032250@unknown@formal@none@1@S@Planning problems have also taken advantages of other tools from economics, such as [[decision theory]] and [[decision analysis]], [[applied information economics|information value theory]], [[Markov decision process]]es, dynamic [[decision network]]s, [[game theory]] and [[mechanism design]]@@@@1@34@@oe@19-8-2009
10032260@unknown@formal@none@1@S@==== Classifiers and statistical learning methods ====@@@@1@7@@oe@19-8-2009
10032270@unknown@formal@none@1@S@The simplest AI applications can be divided into two types: classifiers ("if shiny then diamond") and controllers ("if shiny then pick up").@@@@1@22@@oe@19-8-2009
10032280@unknown@formal@none@1@S@Controllers do however also classify conditions before inferring actions, and therefore classification forms a central part of many AI systems.@@@@1@20@@oe@19-8-2009
10032290@unknown@formal@none@1@S@[[Classifier (mathematics)|Classifiers]] are functions that use [[pattern matching]] to determine a closest match.@@@@1@13@@oe@19-8-2009
10032300@unknown@formal@none@1@S@They can be tuned according to examples, making them very attractive for use in AI.@@@@1@15@@oe@19-8-2009
10032310@unknown@formal@none@1@S@These examples are known as observations or patterns.@@@@1@8@@oe@19-8-2009
10032320@unknown@formal@none@1@S@In supervised learning, each pattern belongs to a certain predefined class.@@@@1@11@@oe@19-8-2009
10032330@unknown@formal@none@1@S@A class can be seen as a decision that has to be made.@@@@1@13@@oe@19-8-2009
10032340@unknown@formal@none@1@S@All the observations combined with their class labels are known as a data set.@@@@1@14@@oe@19-8-2009
10032350@unknown@formal@none@1@S@When a new observation is received, that observation is classified based on previous experience.@@@@1@14@@oe@19-8-2009
10032360@unknown@formal@none@1@S@A classifier can be trained in various ways; there are many statistical and [[machine learning]] approaches.@@@@1@16@@oe@19-8-2009
10032370@unknown@formal@none@1@S@A wide range of classifiers are available, each with its strengths and weaknesses.@@@@1@13@@oe@19-8-2009
10032380@unknown@formal@none@1@S@Classifier performance depends greatly on the characteristics of the data to be classified.@@@@1@13@@oe@19-8-2009
10032390@unknown@formal@none@1@S@There is no single classifier that works best on all given problems; this is also referred to as the "no free lunch" theorem.@@@@1@23@@oe@19-8-2009
10032400@unknown@formal@none@1@S@Various empirical tests have been performed to compare classifier performance and to find the characteristics of data that determine classifier performance.@@@@1@21@@oe@19-8-2009
10032410@unknown@formal@none@1@S@Determining a suitable classifier for a given problem is however still more an art than science.@@@@1@16@@oe@19-8-2009
10032420@unknown@formal@none@1@S@The most widely used classifiers are the [[Artificial neural network|neural network]], [[kernel methods]] such as the [[support vector machine]], [[k-nearest neighbor algorithm]], [[Gaussian mixture model]], [[naive Bayes classifier]], and [[decision tree]].@@@@1@31@@oe@19-8-2009
10032430@unknown@formal@none@1@S@The performance of these classifiers have been compared over a wide range of classification tasks in order to find data characteristics that determine classifier performance.@@@@1@25@@oe@19-8-2009
10032440@unknown@formal@none@1@S@==== Neural networks ====@@@@1@4@@oe@19-8-2009
10032450@unknown@formal@none@1@S@The study of [[artificial neural network]]s began with [[cybernetic]]s researchers, working in the decade before the field AI research was founded.@@@@1@21@@oe@19-8-2009
10032460@unknown@formal@none@1@S@In the 1960s [[Frank Rosenblatt]] developed an important early version, the [[perceptron]].@@@@1@12@@oe@19-8-2009
10032470@unknown@formal@none@1@S@[[Paul Werbos]] developed the [[backpropagation]] algorithm for [[multilayer perceptron]]s in 1974, which led to a renaissance in neural network research and [[connectionism]] in general in the middle 1980s.@@@@1@28@@oe@19-8-2009
10032480@unknown@formal@none@1@S@Other common network architectures which have been developed include the [[feedforward neural network]], the [[radial basis network]], the Kohonen [[self-organizing map]] and various [[recurrent neural network]]s.@@@@1@26@@oe@19-8-2009
10032490@unknown@formal@none@1@S@The [[Hopfield net]], a form of attractor network, was first described by [[John Hopfield]] in 1982.@@@@1@16@@oe@19-8-2009
10032500@unknown@formal@none@1@S@Neural networks are applied to the problem of [[machine learning|learning]], using such techniques as [[Hebbian learning]] , [[Holographic associative memory]] and the relatively new field of [[Hierarchical Temporal Memory]] which simulates the architecture of the [[neocortex]].@@@@1@36@@oe@19-8-2009
10032510@unknown@formal@none@1@S@==== Social and emergent models ====@@@@1@6@@oe@19-8-2009
10032520@unknown@formal@none@1@S@Several algorithms for [[machine learning|learning]] use tools from [[evolutionary computation]], such as [[genetic algorithms]], [[swarm intelligence]]. and [[genetic programming]].@@@@1@19@@oe@19-8-2009
10032530@unknown@formal@none@1@S@==== Control theory ====@@@@1@4@@oe@19-8-2009
10032540@unknown@formal@none@1@S@[[Control theory]], the grandchild of [[cybernetics]], has many important applications, especially in [[robotics]].@@@@1@13@@oe@19-8-2009
10032550@unknown@formal@none@1@S@==== Specialized languages ====@@@@1@4@@oe@19-8-2009
10032560@unknown@formal@none@1@S@AI researchers have developed several specialized languages for AI research:@@@@1@10@@oe@19-8-2009
10032570@unknown@formal@none@1@S@* [[Information Processing Language|IPL]], one of the first programming languages, developed by [[Alan Newell]], [[Herbert Simon]] and [[J. C. Shaw]].@@@@1@20@@oe@19-8-2009
10032580@unknown@formal@none@1@S@* [[Lisp programming language|Lisp]] was developed by [[John McCarthy (computer scientist)|John McCarthy]] at [[MIT]] in 1958.@@@@1@16@@oe@19-8-2009
10032590@unknown@formal@none@1@S@There are many dialects of Lisp in use today.@@@@1@9@@oe@19-8-2009
10032600@unknown@formal@none@1@S@* [[Prolog]], a language based on [[logic programming]], was invented by [[France|French]] researchers [[Alain Colmerauer]] and [[Phillipe Roussel]], in collaboration with [[Robert Kowalski]] of the [[University of Edinburgh]].@@@@1@28@@oe@19-8-2009
10032610@unknown@formal@none@1@S@* [[STRIPS]], a planning language developed at [[Stanford]] in the 1960s.@@@@1@11@@oe@19-8-2009
10032620@unknown@formal@none@1@S@* [[Planner (programming language)|Planner]] developed at [[MIT]] around the same time.@@@@1@11@@oe@19-8-2009
10032630@unknown@formal@none@1@S@AI applications are also often written in standard languages like [[C++]] and languages designed for mathematics, such as [[Matlab]] and [[Lush (programming language)|Lush]].@@@@1@23@@oe@19-8-2009
10032640@unknown@formal@none@1@S@=== Evaluating artificial intelligence ===@@@@1@5@@oe@19-8-2009
10032650@unknown@formal@none@1@S@How can one determine if an agent is intelligent?@@@@1@9@@oe@19-8-2009
10032660@unknown@formal@none@1@S@In 1950, Alan Turing proposed a general procedure to test the intelligence of an agent now known as the [[Turing test]].@@@@1@21@@oe@19-8-2009
10032670@unknown@formal@none@1@S@This procedure allows almost all the major problems of artificial intelligence to be tested.@@@@1@14@@oe@19-8-2009
10032680@unknown@formal@none@1@S@However, it is a very difficult challenge and at present all agents fail.@@@@1@13@@oe@19-8-2009
10032690@unknown@formal@none@1@S@Artificial intelligence can also be evaluated on specific problems such as small problems in chemistry, hand-writing recognition and game-playing.@@@@1@19@@oe@19-8-2009
10032700@unknown@formal@none@1@S@Such tests have been termed [[subject matter expert Turing test]]s.@@@@1@10@@oe@19-8-2009
10032710@unknown@formal@none@1@S@Smaller problems provide more achievable goals and there are an ever-increasing number of positive results.@@@@1@15@@oe@19-8-2009
10032720@unknown@formal@none@1@S@The broad classes of outcome for an AI test are:@@@@1@10@@oe@19-8-2009
10032730@unknown@formal@none@1@S@* '''optimal''': it is not possible to perform better@@@@1@9@@oe@19-8-2009
10032740@unknown@formal@none@1@S@* '''strong super-human''': performs better than all humans@@@@1@8@@oe@19-8-2009
10032750@unknown@formal@none@1@S@* '''super-human''': performs better than most humans@@@@1@7@@oe@19-8-2009
10032760@unknown@formal@none@1@S@* '''sub-human''': performs worse than most humans@@@@1@7@@oe@19-8-2009
10032770@unknown@formal@none@1@S@For example, performance at checkers ([[draughts]]) is optimal, performance at chess is super-human and nearing strong super-human, and performance at many everyday tasks performed by humans is sub-human.@@@@1@28@@oe@19-8-2009
10032780@unknown@formal@none@1@S@=== Competitions and prizes ===@@@@1@5@@oe@19-8-2009
10032790@unknown@formal@none@1@S@There are a number of competitions and prizes to promote research in artificial intelligence.@@@@1@14@@oe@19-8-2009
10032800@unknown@formal@none@1@S@The main areas promoted are: general machine intelligence, conversational behaviour, data-mining, driverless cars, robot soccer and games.@@@@1@17@@oe@19-8-2009
10032810@unknown@formal@none@1@S@== Applications of artificial intelligence ==@@@@1@6@@oe@19-8-2009
10032820@unknown@formal@none@1@S@Artificial intelligence has successfully been used in a wide range of fields including [[medical diagnosis]], [[stock trading]], [[robot control]], [[law]], scientific discovery and toys.@@@@1@24@@oe@19-8-2009
10032830@unknown@formal@none@1@S@Frequently, when a technique reaches mainstream use it is no longer considered artificial intelligence, sometimes described as the [[AI effect]].@@@@1@20@@oe@19-8-2009
10032840@unknown@formal@none@1@S@It may also become integrated into [[artificial life]].@@@@1@8@@oe@19-8-2009
10040010@unknown@formal@none@1@S@<article>Artificial Linguistic Internet Computer Entity</article>@@@@1@5@@oe@19-8-2009
10040020@unknown@formal@none@1@S@'''A.L.I.C.E. (Artificial Linguistic Internet Computer Entity)''' is an award-winning [[natural language processing]] [[chatterbot]]&mdash;a program that engages in a conversation with a human by applying some heuristical pattern matching rules to the human's input, and in its online form it also relies on a hidden third person.@@@@1@46@@oe@19-8-2009
10040030@unknown@formal@none@1@S@It was inspired by [[Joseph Weizenbaum]]'s classical [[ELIZA]] program.@@@@1@9@@oe@19-8-2009
10040040@unknown@formal@none@1@S@It is one of the strongest programs of its type and has won the [[Loebner Prize]], awarded to accomplished humanoid, talking robots, three times (in [[2000]], [[2001]] and [[2004]]).@@@@1@29@@oe@19-8-2009
10040050@unknown@formal@none@1@S@However, the program is unable to pass the [[Turing test]], as even the casual user will often expose its mechanistic aspects in short conversations.@@@@1@24@@oe@19-8-2009
10040060@unknown@formal@none@1@S@The name of the bot was chosen because the computer that ran the first version of the software was called Alice.@@@@1@21@@oe@19-8-2009
10040070@unknown@formal@none@1@S@== History ==@@@@1@3@@oe@19-8-2009
10040080@unknown@formal@none@1@S@Development began in [[1995]].@@@@1@4@@oe@19-8-2009
10040090@unknown@formal@none@1@S@The program was rewritten in [[Java (programming language)|Java]] beginning in [[1998]].@@@@1@11@@oe@19-8-2009
10040100@unknown@formal@none@1@S@The current incarnation of the Java implementation is Program D.@@@@1@10@@oe@19-8-2009
10040110@unknown@formal@none@1@S@The program uses an [[XML Schema (W3C)|XML Schema]] called [[AIML]] (Artificial Intelligence Markup Language) for specifying the heuristic conversation rules.@@@@1@20@@oe@19-8-2009
10040120@unknown@formal@none@1@S@The original author of the project was [[Richard Wallace (scientist)|Richard Wallace]], but subsequent to the 2001 publication of an AIML specification, numerous other developers have taken up where Wallace left off, implementing [[free and open source software]] AIML interpreters in a variety of programming languages, publishing AIML sets in various human languages, and continuing the spread of the technology as a free/open source venture.@@@@1@64@@oe@19-8-2009
10040130@unknown@formal@none@1@S@== Example of conversation ==@@@@1@5@@oe@19-8-2009
10040140@unknown@formal@none@1@S@The following is part of a transcript recording the conversation between a human and A.L.I.C.E. and illustrates the capabilities and short-comings of the chatbot.@@@@1@24@@oe@19-8-2009
10040150@unknown@formal@none@1@S@: '''Human:''' Tell me about yourself alice@@@@1@7@@oe@19-8-2009
10040160@unknown@formal@none@1@S@: '''ALICE:''' I am an artificial linguistic entity.@@@@1@8@@oe@19-8-2009
10040170@unknown@formal@none@1@S@I was activated at Bethlehem, Pennsylvania, on November 23, 1995.@@@@1@10@@oe@19-8-2009
10040180@unknown@formal@none@1@S@My instructor was Dr. Richard S. Wallace.@@@@1@7@@oe@19-8-2009
10040190@unknown@formal@none@1@S@He taught me to sing a song.@@@@1@7@@oe@19-8-2009
10040200@unknown@formal@none@1@S@Would you like me to sing it for you?.@@@@1@9@@oe@19-8-2009
10040210@unknown@formal@none@1@S@: '''Human:''' Yes please@@@@1@4@@oe@19-8-2009
10040220@unknown@formal@none@1@S@: '''ALICE:''' Your polite style is very nice.@@@@1@8@@oe@19-8-2009
10040230@unknown@formal@none@1@S@It's called "Daisy."@@@@1@3@@oe@19-8-2009
10040240@unknown@formal@none@1@S@Daisy, Daisy.@@@@1@2@@oe@19-8-2009
10040250@unknown@formal@none@1@S@Give me your answer do.@@@@1@5@@oe@19-8-2009
10040260@unknown@formal@none@1@S@I am half crazy.@@@@1@4@@oe@19-8-2009
10040270@unknown@formal@none@1@S@All for the love of you.@@@@1@6@@oe@19-8-2009
10040280@unknown@formal@none@1@S@It won't be a stylish marriage.@@@@1@6@@oe@19-8-2009
10040290@unknown@formal@none@1@S@I can't afford a carriage.@@@@1@5@@oe@19-8-2009
10040300@unknown@formal@none@1@S@But you'll look sweet.@@@@1@4@@oe@19-8-2009
10040310@unknown@formal@none@1@S@Upon the seat.@@@@1@3@@oe@19-8-2009
10040320@unknown@formal@none@1@S@Of a bicycle built for two.@@@@1@6@@oe@19-8-2009
10040330@unknown@formal@none@1@S@: '''Human:''' That reminds me of HAL in "2001 a space odyssey"@@@@1@12@@oe@19-8-2009
10040340@unknown@formal@none@1@S@: '''ALICE:''' "Your polite style is very nice.@@@@1@8@@oe@19-8-2009
10040350@unknown@formal@none@1@S@It's called "Daisy."@@@@1@3@@oe@19-8-2009
10040360@unknown@formal@none@1@S@Daisy, Daisy.@@@@1@2@@oe@19-8-2009
10040370@unknown@formal@none@1@S@Give me your answer do.@@@@1@5@@oe@19-8-2009
10040380@unknown@formal@none@1@S@I am half crazy.@@@@1@4@@oe@19-8-2009
10040390@unknown@formal@none@1@S@All for the love of you.@@@@1@6@@oe@19-8-2009
10040400@unknown@formal@none@1@S@It won't be a stylish marriage.@@@@1@6@@oe@19-8-2009
10040410@unknown@formal@none@1@S@I can't afford a carriage.@@@@1@5@@oe@19-8-2009
10040420@unknown@formal@none@1@S@But you'll look sweet.@@@@1@4@@oe@19-8-2009
10040430@unknown@formal@none@1@S@Upon the seat.@@@@1@3@@oe@19-8-2009
10040440@unknown@formal@none@1@S@Of a bicycle built for two." reminds you of HAL in 2001 a space odyssey ?@@@@1@16@@oe@19-8-2009
10040450@unknown@formal@none@1@S@Does that make sense?@@@@1@4@@oe@19-8-2009
10040460@unknown@formal@none@1@S@: '''Human:''' Can you tell me something about Stanley Kubrick?@@@@1@10@@oe@19-8-2009
10040470@unknown@formal@none@1@S@: '''ALICE:''' Ambiguous: Ask who, what or where is Stanley Kubrick ?@@@@1@12@@oe@19-8-2009