Some aspects of synchronization of DFA

Avraham Trahtman

doi:10.1007/s11390-008-9165-4

Some aspects of synchronization of DFA

Avraham Trahtman

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

A word w is called synchronizing (recurrent, reset, directable) word of deterministic finite automata (DFA) if w brings all states of the automaton to a unique state. According to the famous conjecture of Černý from 1964, every n-state synchronizing automaton possesses a synchronizing word of length at most (n-1) ². The problem is still open. It will be proved that the Černý conjecture holds good for synchronizing DFA with transition monoid having no involutions and for every n-state (n > 2) synchronizing DFA with transition monoid having only trivial subgroups the minimal length of synchronizing word is not greater than (n-1) ²/2. The last important class of DFA involved and studied by Schǔtzenberger is called aperiodic; its automata accept precisely star-free languages. Some properties of an arbitrary synchronizing DFA were established. See http://www.cs.biu.ac.il/~trakht/syn.html .

Original language	English
Pages (from-to)	719-727
Number of pages	9
Journal	Journal of Computer Science and Technology
Volume	23
Issue number	5
DOIs	https://doi.org/10.1007/s11390-008-9165-4
State	Published - Sep 2008

Keywords

Aperiodic semigroup
Deterministic finite automata (DFA)
Synchronization
Černý conjecture

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10.1007/s11390-008-9165-4

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abstract = "A word w is called synchronizing (recurrent, reset, directable) word of deterministic finite automata (DFA) if w brings all states of the automaton to a unique state. According to the famous conjecture of {\v C}ern{\'y} from 1964, every n-state synchronizing automaton possesses a synchronizing word of length at most (n-1) 2. The problem is still open. It will be proved that the {\v C}ern{\'y} conjecture holds good for synchronizing DFA with transition monoid having no involutions and for every n-state (n > 2) synchronizing DFA with transition monoid having only trivial subgroups the minimal length of synchronizing word is not greater than (n-1) 2/2. The last important class of DFA involved and studied by Schǔtzenberger is called aperiodic; its automata accept precisely star-free languages. Some properties of an arbitrary synchronizing DFA were established. See http://www.cs.biu.ac.il/~trakht/syn.html .",

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Some aspects of synchronization of DFA

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Keywords

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