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Computational Complexity of Certain Problems Related to Carefully Synchronizing Words for Partial Automata and Directing Words for Nondeterministic Automata

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Abstract

We show that the problem of checking careful synchronizability of partial finite automata is PSPACE-complete. Also the problems of checking D 1-, D 2-, and D 3-directability of nondeterministic finite automata are PSPACE-complete; moreover, the restrictions of all these problems to automata with two input letters remain PSPACE-complete.

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Acknowledgements

The author is grateful to Dr. D. Ananichev and Prof. M. Volkov for valuable help and to the anonymous reviewers of the conference version [12] of the present paper for their detailed reviews with a number of useful recommendations.

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  1. Institute of Mathematics and Computer Science, Ural Federal University, 620000, Ekaterinburg, Russia

    Pavel Martyugin

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  1. Pavel Martyugin
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Correspondence to Pavel Martyugin.

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The author acknowledges support from the Russian Foundation for Basic Research, grant 13-01-00852, and by the Presidential Program for young researchers, grant MK-266.2012.1.

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Martyugin, P. Computational Complexity of Certain Problems Related to Carefully Synchronizing Words for Partial Automata and Directing Words for Nondeterministic Automata. Theory Comput Syst 54, 293–304 (2014). https://doi.org/10.1007/s00224-013-9516-6

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