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Operational State Complexity under Parikh Equivalence

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Descriptional Complexity of Formal Systems (DCFS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8614))

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Abstract

We investigate, under Parikh equivalence, the state complexity of some language operations which preserve regularity. For union, concatenation, Kleene star, complement, intersection, shuffle, and reversal, we obtain a polynomial state complexity over any fixed alphabet, in contrast to the intrinsic exponential state complexity of some of these operations in the classical version. For projection we prove a superpolynomial state complexity, which is lower than the exponential one of the corresponding classical operation. We also prove that for each two deterministic automata A and B it is possible to obtain a deterministic automaton with a polynomial number of states whose accepted language has as Parikh image the intersection of the Parikh images of the languages accepted by A and B. Finally, we prove that for each finite set there exists a small context-free grammar defining a language with the same Parikh image.

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Università degli Studi di Milano, Italy

    Giovanna J. Lavado & Giovanni Pighizzini

  2. Helsinki Institute for Information Technology (HIIT), P.O. Box 15600, 00076, Aalto, Finland

    Shinnosuke Seki

  3. Department of Information and Computer Science, Aalto University, P.O. Box 15400, FI-00076, Aalto, Finland

    Shinnosuke Seki

Authors
  1. Giovanna J. Lavado
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  2. Giovanni Pighizzini
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  3. Shinnosuke Seki
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Editor information

Editors and Affiliations

  1. Department of Computer Science, The University of Western Ontario, N6A 5B7, London, Ontario, Canada

    Helmut Jürgensen

  2. Department of Mathematics and TUCS, University of Turku, 20014, Turku, Finland

    Juhani Karhumäki

  3. University of Turku, Fi-20014, Turku, Finland

    Alexander Okhotin

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© 2014 Springer International Publishing Switzerland

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Lavado, G.J., Pighizzini, G., Seki, S. (2014). Operational State Complexity under Parikh Equivalence. In: Jürgensen, H., Karhumäki, J., Okhotin, A. (eds) Descriptional Complexity of Formal Systems. DCFS 2014. Lecture Notes in Computer Science, vol 8614. Springer, Cham. https://doi.org/10.1007/978-3-319-09704-6_26

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  • DOI: https://doi.org/10.1007/978-3-319-09704-6_26

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09703-9

  • Online ISBN: 978-3-319-09704-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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