eng
episciences.org
Discrete Mathematics & Theoretical Computer Science
1365-8050
2007-01-01
Vol. 9 no. 2
10.46298/dmtcs.395
395
journal article
The \v CernĂ½ conjecture for aperiodic automata
A. N. Trahtman
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. Cerny 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 Cerny conjecture holds true.
https://dmtcs.episciences.org/395/pdf
[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]