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Careful Synchronization of One-Cluster Automata (2311.15020v1)

Published 25 Nov 2023 in cs.FL and cs.CC

Abstract: In this paper we investigate careful synchronization of one-cluster partial automata. First we prove that in general case the shortest carefully synchronizing word for such automata is of length $2\frac{n}{2} + 1$, where $n$ is the number of states of an automaton. Additionally we prove that checking whether a given one-cluster partial automaton is carefully synchronizing is NP-hard even in the case of binary alphabet.

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