Please use this identifier to cite or link to this item:
http://elar.urfu.ru/handle/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://elar.urfu.ru/handle/10995/111871 |
Access: | info:eu-repo/semantics/openAccess |
SCOPUS ID: | 79952131123 |
PURE ID: | 37846954 |
ISSN: | 0129-0541 |
Appears in Collections: | Научные публикации ученых УрФУ, проиндексированные в SCOPUS и WoS CC |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
2-s2.0-79952131123.pdf | 259,74 kB | Adobe PDF | View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.