Trahtman, A. N. - The \v Cerný conjecture for aperiodic automata

dmtcs:395 - Discrete Mathematics & Theoretical Computer Science, January 1, 2007, Vol. 9 no. 2
The \v Cerný conjecture for aperiodic automata

Authors: Trahtman, A. N.

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.


Source : oai:HAL:hal-00966534v1
Volume: Vol. 9 no. 2
Published on: January 1, 2007
Submitted on: March 26, 2015
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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