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Mortality and Synchronization of Unambiguous Finite Automata

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Combinatorics on Words (WORDS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11682))

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Abstract

We study mortal words and words of minimum non-zero rank (in particular, synchronizing words) in strongly connected unambiguous automata. We show that every n-state strongly connected unambiguous automaton admits a word of minimum non-zero rank of length at most \(n^5\), and this word can be found in polynomial time. We show that for words of minimum rank this upper bound can be lowered to \(O(n^3 (\log n)^4)\) for prefix automata of finite codes and to \(O(n^3 \log n)\) for prefix automata of complete finite codes. We also provide quadratic lower bounds on the length of shortest mortal words for several classes of deterministic automata.

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Acknowledgments

I am grateful to Dominique Perrin for many helpful discussions and his constant interest to this work. I also thank Vladimir Gusev, Stefan Kiefer and Elena Pribavkina for their useful comments on an early version of this manuscript, and anonymous reviewers for their suggestions on the presentation of the paper.

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Authors and Affiliations

  1. LIGM, Université Paris-Est, Marne-la-Vallée, France

    Andrew Ryzhikov

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  1. Andrew Ryzhikov
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Correspondence to Andrew Ryzhikov .

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Editors and Affiliations

  1. Loughborough University, Loughborough, UK

    Robert Mercaş

  2. Loughborough University, Loughborough, UK

    Daniel Reidenbach

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Ryzhikov, A. (2019). Mortality and Synchronization of Unambiguous Finite Automata. In: Mercaş, R., Reidenbach, D. (eds) Combinatorics on Words. WORDS 2019. Lecture Notes in Computer Science(), vol 11682. Springer, Cham. https://doi.org/10.1007/978-3-030-28796-2_24

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  • DOI: https://doi.org/10.1007/978-3-030-28796-2_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-28795-5

  • Online ISBN: 978-3-030-28796-2

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