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Binary Completely Reachable Automata

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LATIN 2022: Theoretical Informatics (LATIN 2022)

Abstract

We characterize complete deterministic finite automata with two input letters in which every non-empty set of states occurs as the image of the whole state set under the action of a suitable input word. The characterization leads to a polynomial-time algorithm for recognizing this class of automata.

The authors were supported by the Ministry of Science and Higher Education of the Russian Federation, project FEUZ-2020-0016.

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Notes

  1. 1.

    In fact, our definition is the semigroup version of the notion of a Cayley digraph, but this makes no difference since in a finite group, every subsemigroup is a subgroup.

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Acknowledgement

We thank the anonymous reviewers for their careful reading of our paper and their many useful comments and suggestions.

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Correspondence to Mikhail V. Volkov .

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Casas, D., Volkov, M.V. (2022). Binary Completely Reachable Automata. In: Castañeda, A., Rodríguez-Henríquez, F. (eds) LATIN 2022: Theoretical Informatics. LATIN 2022. Lecture Notes in Computer Science, vol 13568. Springer, Cham. https://doi.org/10.1007/978-3-031-20624-5_21

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  • DOI: https://doi.org/10.1007/978-3-031-20624-5_21

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