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On the Complexity of Hopcroft’s State Minimization Algorithm

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Implementation and Application of Automata (CIAA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3317))

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Abstract

Hopcroft’s algorithm for minimizing a deterministic automaton has complexity O(n log n). We show that this complexity bound is tight. More precisely, we provide a family of automata of size n = 2k on which the algorithm runs in time k2k. These automata have a very simple structure and are built over a one-letter alphabet. Their sets of final states are defined by de Bruijn words.

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Author information

Authors and Affiliations

  1. Institut Gaspard Monge, Université de Marne-la-Vallée,  

    Jean Berstel

  2. LIAFA, Université Paris 7,  

    Olivier Carton

Authors
  1. Jean Berstel
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  2. Olivier Carton
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Manitoba, R3T 2N2, Winnipeg, MB, Canada

    Michael Domaratzki

  2. Department of Mathematics, University of Turku, Finland

    Alexander Okhotin

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

    Kai Salomaa

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

    Sheng Yu

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© 2005 Springer-Verlag Berlin Heidelberg

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Berstel, J., Carton, O. (2005). On the Complexity of Hopcroft’s State Minimization Algorithm. In: Domaratzki, M., Okhotin, A., Salomaa, K., Yu, S. (eds) Implementation and Application of Automata. CIAA 2004. Lecture Notes in Computer Science, vol 3317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30500-2_4

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  • DOI: https://doi.org/10.1007/978-3-540-30500-2_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24318-2

  • Online ISBN: 978-3-540-30500-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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