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International Conference on Descriptional Complexity of Formal Systems

DCFS 2018: Descriptional Complexity of Formal Systems pp 200–211Cite as

Cycle Height of Finite Automata

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10952))

Abstract

A nondeterministic finite automaton (NFA) A has cycle height \(\mathcal {K}\) if any computation of A can visit at most \(\mathcal {K}\) cycles, and A has finite cycle height if it has cycle height \(\mathcal {K}\) for some \(\mathcal {K}\). We give a polynomial time algorithm to decide whether an NFA has finite cycle height and, in the positive case, to compute its optimal cycle height. Nondeterministic finite automata of finite cycle height recognize the polynomial density regular languages.

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Notes

  1. 1.

    By non-equivalent cycles we mean cycles that are not permutations of each other. The notion will be defined formally in Sect. 2.

  2. 2.

    Strictly speaking, the t-tiered words are defined in [15] only with respect to a DFA.

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Acknowledgments

Research supported by NSERC grant OGP0147224.

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Authors and Affiliations

  1. School of Computing, Queen’s University, Kingston, ON, K7L 2N8, Canada

    Chris Keeler & Kai Salomaa

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  1. Chris Keeler
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  2. Kai Salomaa
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Correspondence to Chris Keeler .

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Editors and Affiliations

  1. Department of Mathematics and Computing Science, Saint Mary’s University, Halifax, Nova Scotia, Canada

    Stavros Konstantinidis

  2. Dipartimento di Informatica e Comunicazi, Universita degli Studi di Milano, Milan, Italy

    Giovanni Pighizzini

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Keeler, C., Salomaa, K. (2018). Cycle Height of Finite Automata. In: Konstantinidis, S., Pighizzini, G. (eds) Descriptional Complexity of Formal Systems. DCFS 2018. Lecture Notes in Computer Science(), vol 10952. Springer, Cham. https://doi.org/10.1007/978-3-319-94631-3_17

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  • DOI: https://doi.org/10.1007/978-3-319-94631-3_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-94630-6

  • Online ISBN: 978-3-319-94631-3

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