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Aperiodic finite state automaton : ウィキペディア英語版
Aperiodic finite state automaton
An aperiodic finite-state automaton is a finite-state automaton whose transition monoid is aperiodic.
==Properties==
A regular language is star-free if and only if it is accepted by an automaton with a finite and aperiodic transition monoid. This result of algebraic automata theory is due to Marcel-Paul Schützenberger.
A counter-free language is a regular language for which there is an integer ''n'' such that for all words ''x'', ''y'', ''z'' and integers ''m'' ≥ ''n'' we have ''xy''''m''''z'' in ''L'' if and only if ''xy''''n''''z'' in ''L''. A counter-free automaton is a finite-state automaton which accepts a counter-free language. A finite-state automaton is counter-free if and only if it is aperiodic.
An aperiodic automaton satisfies the Černý conjecture.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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