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A New Technique for Reachability of States in Concatenation Automata

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Descriptional Complexity of Formal Systems (DCFS 2018)

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Abstract

We present a new technique for demonstrating the reachability of states in deterministic finite automata representing the concatenation of two languages. Such demonstrations are a necessary step in establishing the state complexity of the concatenation of two languages, and thus in establishing the state complexity of concatenation as an operation. Typically, ad-hoc induction arguments are used to show particular states are reachable in concatenation automata. We prove some results that seem to capture the essence of many of these induction arguments. Using these results, reachability proofs in concatenation automata can often be done more simply and without using induction directly.

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Acknowledgements

I thank Jason Bell, Janusz Brzozowski and the anonymous referees for proofreading and helpful comments. This work was supported by the Natural Sciences and Engineering Research Council of Canada under grant No. OGP0000871.

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Authors and Affiliations

  1. Department of Pure Mathematics, University of Waterloo, Waterloo, Canada

    Sylvie Davies

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  1. Sylvie Davies
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Correspondence to Sylvie Davies .

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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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Davies, S. (2018). A New Technique for Reachability of States in Concatenation 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_7

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  • DOI: https://doi.org/10.1007/978-3-319-94631-3_7

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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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