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Reversal on Regular Languages and Descriptional Complexity

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Descriptional Complexity of Formal Systems (DCFS 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8031))

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Abstract

We study the problem stated as follows: which values in the range from logn to 2n may be obtained as the state complexity of the reverse of a regular language represented by a minimal deterministic automaton of n states? In the main result of this paper we use an alphabet of size 2n − 2 to show that the entire range of complexities may be produced for any n. This considerably improves an analogous result from the literature that uses an alphabet of size 2n. We also provide some partial results for the case of a binary alphabet.

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Authors and Affiliations

  1. Institute of Computer Science, Faculty of Science, P.J. Šafárik University, Jesenná 5, 040 01, Košice, Slovakia

    Juraj Šebej

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  1. Juraj Šebej
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Editors and Affiliations

  1. Department of Computer Science, Middlesex College, Western University, N6A 5B7, London, ON, Canada

    Helmut Jurgensen

  2. Departamento de Ciência de Computadores, Universidade do Porto, Faculdade de Ciências, Rua do Campo Alegre 1021-1055,, 4169-007, Porto, Portugal

    Rogério Reis

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Šebej, J. (2013). Reversal on Regular Languages and Descriptional Complexity. In: Jurgensen, H., Reis, R. (eds) Descriptional Complexity of Formal Systems. DCFS 2013. Lecture Notes in Computer Science, vol 8031. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39310-5_25

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  • DOI: https://doi.org/10.1007/978-3-642-39310-5_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39309-9

  • Online ISBN: 978-3-642-39310-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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