Abstract
A complete deterministic finite automaton in which every non-empty subset of the state set occurs as the image of the whole state set under the action of a suitable input word is called completely reachable. We characterize completely reachable automata in terms of certain directed graphs.
Supported by the Russian Foundation for Basic Research, grant no. 16-01-00795, the Russian Ministry of Education and Science, project no. 1.3253.2017, and the Competitiveness Enhancement Program of Ural Federal University.
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Bondar, E.A., Volkov, M.V.: Completely Reachable Automata. In: Câmpeanu, C., Manea, F., Shallit, J. (eds.) DCFS 2016. LNCS, vol. 9777, pp. 1–17. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-41114-9_1
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Acknowledgements
The authors are extremely grateful to the anonymous referees for useful remarks and a number of interesting suggestions. Due to space constraints, we have not been in a position to follow all these suggestions in the proceedings paper but we certainly plan to include the suggested enhancements in its extended version.
The authors also thank Pedro V. Silva for a stimulating discussion that has helped us to find yet another construction for a graph associated with a given DFA such that the strong connectivity of the graph is equivalent to the complete reachability of the DFA. The alternative construction, which is more succinct than the one presented here, will also be included in the extended version of this paper.
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Bondar, E.A., Volkov, M.V. (2018). A Characterization of Completely Reachable Automata. In: Hoshi, M., Seki, S. (eds) Developments in Language Theory. DLT 2018. Lecture Notes in Computer Science(), vol 11088. Springer, Cham. https://doi.org/10.1007/978-3-319-98654-8_12
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DOI: https://doi.org/10.1007/978-3-319-98654-8_12
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