Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/111871
Title: A Quadratic Upper Bound on the Size of a Synchronizing Word in One-Cluster Automata
Authors: Béal, M. -P.
Berlinkov, M. V.
Perrin, D.
Issue Date: 2011
Publisher: World Scientific Pub Co Pte Lt
Citation: Béal M. -P. A Quadratic Upper Bound on the Size of a Synchronizing Word in One-Cluster Automata / M. -P. Béal, M. V. Berlinkov, D. Perrin // International Journal of Foundations of Computer Science. — 2011. — Vol. 22. — Iss. 2. — P. 277-288.
Abstract: 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. © 2011 World Scientific Publishing Company.
Keywords: ČERNÝ'S CONJECTURE
ROAD COLORING PROBLEM
SYNCHRONIZED AUTOMATA
URI: http://hdl.handle.net/10995/111871
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 79952131123
ISSN: 0129-0541
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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