Abstract
A word w over an alphabet ∑ is n-synchronizing if it resets every (n∈+∈1)-state synchronizing automaton over this alphabet. For a fixed n and ∑, 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|∑| 2, which improves the lower bound known so far. © 2008 Springer-Verlag Berlin Heidelberg.
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CITATION STYLE
Gawrychowski, P., & Kisielewicz, A. (2008). 2-Synchronizing words. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5196 LNCS, pp. 221–231). https://doi.org/10.1007/978-3-540-88282-4_21
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