Bibliographic Details
| Title: |
The Černý Conjecture for Aperiodic Automata. |
| Authors: |
Trahtman, A. N.1 |
| Source: |
Discrete Mathematics & Theoretical Computer Science (DMTCS). Dec2007, Vol. 9 Issue 2, p3-10. 8p. |
| Subjects: |
Sequential machine theory, Machine theory, Algorithms, Formal languages, Language & languages |
| Abstract: |
A word w is called a synchronizing (recurrent, reset, directable) word of a deterministic finite automaton (DFA) if w brings all states of the automaton to some specific state; a DFA that has a synchronizing word is said to be synchronizable. Černý conjectured in 1964 that every n-state synchronizable DFA possesses a synchronizing word of length at most (n-1)². We consider automata with aperiodic transition monoid (such automata are called aperiodic). We show that every synchronizable n-state aperiodic DFA has a synchronizing word of length at most n(n - 1)/2. Thus, for aperiodic automata as well as for automata accepting only star-free languages, the ČCerný conjecture holds true. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
