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Experiments with Synchronizing Automata

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Implementation and Application of Automata (CIAA 2016)

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Abstract

We have improved an algorithm generating synchronizing automata with a large length of the shortest reset words. This has been done by refining some known results concerning bounds on the reset length. Our improvements make possible to consider a number of conjectures and open questions concerning synchronizing automata, checking them for automata with a small number of states and discussing the results. In particular, we have verified the Černý conjecture for all binary automata with at most 12 states, and all ternary automata with at most 8 states.

A. Kisielewicz—Supported in part by the National Science Centre, Poland under project number 2012/07/B/ST1/03318.

J. Kowalski—Supported in part by the National Science Centre, Poland under project number 2015/17/B/ST6/01893.

M. Szykuła—Supported in part by the National Science Centre, Poland under project number 2013/09/N/ST6/01194.

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Notes

  1. 1.

    Personal communication.

  2. 2.

    Personal communication, unpublished.

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Acknowledgments

We thank Mikhail Volkov for suggesting Conjecture 4, and Mikhail Berlinkov for observing that the bound for one-cluster automata can be improved for periodic subsets on the cycle, which leaded to an improvement of our algorithm. We thank also Vojtěch Vorel for discussing the problem of avoiding states and sharing the series. The main part of the computations was performed on a grid that belongs to Institute of Computer Science of Jagiellonian University (thanks to Adam Roman).

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Wrocław, Wrocław, Poland

    Andrzej Kisielewicz, Jakub Kowalski & Marek Szykuła

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  1. Andrzej Kisielewicz
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  2. Jakub Kowalski
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  3. Marek Szykuła
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Correspondence to Marek Szykuła .

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Editors and Affiliations

  1. Yonsei University, Seoul, Korea (Republic of)

    Yo-Sub Han

  2. Queen's University , Kingston, Ontario, Canada

    Kai Salomaa

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Kisielewicz, A., Kowalski, J., Szykuła, M. (2016). Experiments with Synchronizing Automata. In: Han, YS., Salomaa, K. (eds) Implementation and Application of Automata. CIAA 2016. Lecture Notes in Computer Science(), vol 9705. Springer, Cham. https://doi.org/10.1007/978-3-319-40946-7_15

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  • DOI: https://doi.org/10.1007/978-3-319-40946-7_15

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