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Synchronization Problems in Automata Without Non-trivial Cycles

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Implementation and Application of Automata (CIAA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10329))

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Abstract

We study the computational complexity of various problems related to synchronization of weakly acyclic automata, a subclass of widely studied aperiodic automata. We provide upper and lower bounds on the length of a shortest word synchronizing a weakly acyclic automaton or, more generally, a subset of its states, and show that the problem of approximating this length is hard. We also show inapproximability of the problem of computing the rank of a subset of states in a binary weakly acyclic automaton and prove that several problems related to recognizing a synchronizing subset of states in such automata are NP-complete.

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Acknowledgments

We would like to thank Vladimir Gusev and Ilia Fridman for very useful discussions, and Mikhail V. Volkov and anonymous reviewers for their great contribution to the improvement of the paper.

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Authors and Affiliations

  1. Laboratoire G-SCOP, Université Grenoble Alpes, 38031, Grenoble, France

    Andrew Ryzhikov

  2. United Institute of Informatics Problems of NASB, 220012, Minsk, Belarus

    Andrew Ryzhikov

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  1. Andrew Ryzhikov
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Correspondence to Andrew Ryzhikov .

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Editors and Affiliations

  1. LIGM (UMR 8049), CNRS, Université Paris-Est, Marne-la-Vallée Cedex 2, France

    Arnaud Carayol

  2. LIGM (UMR 8049), Université Paris-Est, Marne-la-Vallée Cedex 2, France

    Cyril Nicaud

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Ryzhikov, A. (2017). Synchronization Problems in Automata Without Non-trivial Cycles. In: Carayol, A., Nicaud, C. (eds) Implementation and Application of Automata. CIAA 2017. Lecture Notes in Computer Science(), vol 10329. Springer, Cham. https://doi.org/10.1007/978-3-319-60134-2_16

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  • DOI: https://doi.org/10.1007/978-3-319-60134-2_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-60133-5

  • Online ISBN: 978-3-319-60134-2

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