episciences.org_395_20230320163441159
20230320163441159
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
Discrete Mathematics & Theoretical Computer Science
13658050
01
01
2007
Vol. 9 no. 2
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 nstate synchronizable DFA possesses a synchronizing word of length at most (n1)2. We consider automata with aperiodic transition monoid (such automata are called aperiodic). We show that every synchronizable nstate aperiodic DFA has a synchronizing word of length at most n(n1)/2. Thus, for aperiodic automata as well as for automata accepting only starfree languages, the Cerny conjecture holds true.
01
01
2007
395
https://hal.science/hal00966534v1
10.46298/dmtcs.395
https://dmtcs.episciences.org/395

https://dmtcs.episciences.org/395/pdf

https://dmtcs.episciences.org/395/pdf