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State Complexity of Basic Operations on Finite Languages

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Automata Implementation (WIA 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2214))

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Abstract

The state complexity of basic operations on regular languages has been studied in [9],[10],[11]. Here we focus on finite languages. We show that the catenation of two finite languages accepted by an mstate and an n-state DFA, respectively, with m > n is accepted by a DFA of (m − n + 3)2n−2 − 1 states in the two-letter alphabet case, and this bound is shown to be reachable. We also show that the tight upperbounds for the number of states of a DFA that accepts the star of an n-state finite language is 2n−3 + 2n−4 in the two-letter alphabet case. The same bound for reversal is 3 · 2p−1 − 1 when n is even and 2p − 1 when n is odd. Results for alphabets of an arbitrary size are also obtained. These upper-bounds for finite languages are strictly lower than the corresponding ones for general regular languages.

The work reported here has been supported by the Natural Sciences and Engineering Research Council of Canada Grants OGP0041630 and OGP0147224.

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Author information

Authors and Affiliations

  1. Fundamentals of Computer Science Department, Faculty of Mathematics University of Bucharest, Romania

    C. Câmpeanu

  2. Department of Computer Science, University of South Carolina, Columbia, SC, 29208, USA

    K. Culik II

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

    Kai Salomaa & Sheng Yu

Authors
  1. C. Câmpeanu
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  2. K. Culik II
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  3. Kai Salomaa
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  4. Sheng Yu
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Editor information

Editors and Affiliations

  1. Universität Potsdam, Institut für Informatik, August-Bebel-Straße 89, 14482, Potsdam, Germany

    Oliver Boldt

  2. Institut für Informatik, Universität Potsdam, Potsdam

    Helmut Jürgensen

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

    Helmut Jürgensen

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© 2001 Springer-Verlag Berlin Heidelberg

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Câmpeanu, C., Culik, K., Salomaa, K., Yu, S. (2001). State Complexity of Basic Operations on Finite Languages. In: Boldt, O., Jürgensen, H. (eds) Automata Implementation. WIA 1999. Lecture Notes in Computer Science, vol 2214. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45526-4_6

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  • DOI: https://doi.org/10.1007/3-540-45526-4_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42812-1

  • Online ISBN: 978-3-540-45526-4

  • eBook Packages: Springer Book Archive

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