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Article Dans Une Revue International Journal of Foundations of Computer Science Année : 2011

A quadratic upper bound on the size of a synchronizing word in one-cluster automata

Résumé

Černý's conjecture asserts the existence of a synchronizing word of length at most (n-1)² for any synchronized n-state deterministic automaton. We prove a quadratic upper bound on the length of a synchronizing word for any synchronized n-state deterministic automaton satisfying the following additional property: there is a letter a such that for any pair of states p, q, one has p*ar = q*as for some integers r, s (for a state p and a word w, we denote by p*w the state reached from p by the path labeled w). As a consequence, we show that for any finite synchronized prefix code with an n-state decoder, there is a synchronizing word of length O(n²). This applies in particular to Huffman codes.
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Dates et versions

hal-00619778 , version 1 (24-02-2013)

Identifiants

Citer

Marie-Pierre Béal, Mikhail V. Berlinkov, Dominique Perrin. A quadratic upper bound on the size of a synchronizing word in one-cluster automata. International Journal of Foundations of Computer Science, 2011, 22 (2), pp.277-288. ⟨10.1142/S0129054111008039⟩. ⟨hal-00619778⟩
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