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Careful synchronization of partial deterministic finite automata

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Abstract

We approach the task of computing a carefully synchronizing word of minimum length for a given partial deterministic automaton, encoding the problem as an instance of SAT and invoking a SAT solver. Our experiments demonstrate that this approach gives satisfactory results for automata with up to 100 states even if very modest computational resources are used. We compare our results with the ones obtained by the first author for exact synchronization, which is another version of synchronization studied in the literature, and draw some theoretical conclusions.

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Notes

  1. It should be mentioned that Rystsov [30] used the term ‘synchronizing word’ for what we call ‘carefully synchronizing word’, following Martyugin [20,21,22,23,24]. The authors are grateful to Dr. Pavel Panteleev who drew their attention to Rystsov’s paper.

  2. We refer the reader to [5,  Chapters 3 and 10] for a detailed account of profound connections between codes and automata.

  3. It is fair to say that encodings in [33, 35] were designed to handle much more general nondeterministic automata so it is not a surprise that those encodings were bulkier than the present one.

  4. Türker [40] uses the term ‘reset sequence’ for what we call ‘exactly synchronizing word’.

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Acknowledgements

We are grateful to the reviewers for a number of valuable remarks and suggestions.

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Authors and Affiliations

  1. Faculty of Electronic Engineering, Menoufia University, Menouf, Egypt

    Hanan Shabana

  2. Institute of Natural Sciences and Mathematics, Ural Federal University, Ekaterinburg, Russia

    Hanan Shabana & M. V. Volkov

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  1. Hanan Shabana
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  2. M. V. Volkov
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Correspondence to M. V. Volkov.

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Supported by the Ministry of Science and Higher Education of the Russian Federation, project FEUZ-2020-0016.

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Shabana, H., Volkov, M.V. Careful synchronization of partial deterministic finite automata. Acta Informatica 59, 479–504 (2022). https://doi.org/10.1007/s00236-022-00433-1

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