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• W2149252886 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 ·a r = q ·a s 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(n 2). This applies in particular to Huffman codes." @default.
• W2149252886 created "2016-06-24" @default.
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• W2149252886 date "2009-01-01" @default.
• W2149252886 modified "2023-10-18" @default.
• W2149252886 title "A Quadratic Upper Bound on the Size of a Synchronizing Word in One-Cluster Automata" @default.
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• W2149252886 doi "https://doi.org/10.1007/978-3-642-02737-6_6" @default.
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