Reset sequences for monotonic automata
SIAM Journal on Computing
An introduction to symbolic dynamics and coding
An introduction to symbolic dynamics and coding
The NP-completeness of the Road Coloring Problem
Information Processing Letters
An algorithm for road coloring
IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
An algorithm for road coloring
Journal of Discrete Algorithms
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After Trahtman in his brilliant paper [10] solved the Road Coloring Problem, a couple of new problems have arisen in the field of synchronizing automata. Some of them naturally extends questions related to the 'classical' version of synchronization. Particulary, it is known that the problem of finding the synchronizing word of a given length for a given automaton is NP-complete. Volkov [11] asked, what is the complexity of the following problem: given a constant out-degree digraph (possibly with multiple edges) and a natural number m, does there exist a synchronizing word of length m for some synchronizing labeling of G. In this paper we show that this decision version of the Road Coloring Problem is NP-complete.