Abstract
Under the assumption P≠NP, we prove that two natural problems from the theory of synchronizing automata cannot be solved in polynomial time. The first problem is to decide whether a given reachable partial automaton is synchronizing. The second one is, given an n-state binary complete synchronizing automaton, to compute its reset threshold within performance ratio less than d ln (n) for a specific constant d > 0.
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Berlinkov, M.V. (2014). On Two Algorithmic Problems about Synchronizing Automata. In: Shur, A.M., Volkov, M.V. (eds) Developments in Language Theory. DLT 2014. Lecture Notes in Computer Science, vol 8633. Springer, Cham. https://doi.org/10.1007/978-3-319-09698-8_6
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DOI: https://doi.org/10.1007/978-3-319-09698-8_6
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