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.
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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We thank the anonymous reviewers for their careful reading of our paper and their many useful comments and suggestions.
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Casas, D., Volkov, M.V. (2022). Binary Completely Reachable Automata. In: Castañeda, A., RodrÃguez-HenrÃquez, 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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