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automaton


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A general term for a device that mechanically processes an input string with the aim either of deciding whether it belongs to some set of strings (i.e. to a formal language) or of producing an output string.

There are two senses in which an automaton A is said to recognize (or accept) a language L: for any input string w,(a) A halts and indicates that it accepts or rejects w, corresponding with whether or not wL;(b) A halts if wL and fails to halt otherwise.In the case of Turing machines, the languages recognizable in sense (a) and the weaker sense (b) are the recursive sets and the recursively enumerable sets, respectively.

(a) A halts and indicates that it accepts or rejects w, corresponding with whether or not wL;

(b) A halts if wL and fails to halt otherwise.

Turing machines are a particular kind of automaton. Other kinds include the finite-state automaton, pushdown automaton, and linear-bounded automaton. Sequential machines are automata that produce an output string. According to the Church-Turing thesis, if a language is recognizable (in either of the above senses) by any kind of automaton, it is so recognizable by a Turing machine.

Subjects: Computing.


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