2-Synchronizing Words

Authors:
Paweł Gawrychowski;Andrzej Kisielewicz
Affiliations:
Institute of Computer Science, University of Wrocław, Wrocław, Poland 50-383;Institute of Mathematics, University of Wrocław, Wrocław, Poland 50-384
Venue:
Language and Automata Theory and Applications
Year:
2008

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Abstract

A word wover an alphabet Σis n-synchronizing if it resets every (n+ 1)-state synchronizing automaton over this alphabet. For a fixed nand Σ, n-synchronizing words can be recognized in polynomial time, yet no practical algorithm is known. In this paper we show that one cannot expect to find such an algorithm. We prove that the problem of recognizing 2-synchronizing words, where the input consists of a word and an alphabet, is co-NP-complete. We also show that the length of a 2-synchronizing word is at least 2|Σ|2, which improves the lower bound known so far.