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State Complexity of k-Union and k-Intersection for Prefix-Free Regular Languages

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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 investigate the state complexity of multiple unions and of multiple intersections for prefix-free regular languages. Prefix-free deterministic finite automata have their own unique structural properties that are crucial for obtaining state complexity upper bounds that are improved from those for general regular languages. We present a tight lower bound construction for k-union using an alphabet of size k + 1 and for k-intersection using a binary alphabet. We prove that the state complexity upper bound for k-union cannot be reached by languages over an alphabet with less than k symbols. We also give a lower bound construction for k-union using a binary alphabet that is within a constant factor of the upper bound.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Yonsei University, 50, Yonsei-Ro, Seodaemun-Gu, Seoul, 120-749, Republic of Korea

    Hae-Sung Eom & Yo-Sub Han

  2. School of Computing, Queen’s University, Kingston, Ontario, K7L 3N6, Canada

    Kai Salomaa

Authors
  1. Hae-Sung Eom
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  2. Yo-Sub Han
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  3. Kai Salomaa
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Editor information

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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Eom, HS., Han, YS., Salomaa, K. (2013). State Complexity of k-Union and k-Intersection for Prefix-Free Regular Languages. 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_9

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  • DOI: https://doi.org/10.1007/978-3-642-39310-5_9

  • 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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