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Hopcroft’s Minimization Technique: Queues or Stacks?

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Implementation and Applications of Automata (CIAA 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5148))

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Abstract

We consider the absolute worst case time complexity for Hopcroft’s minimization algorithm applied to unary languages (or a modification of this algorithm for cover automata minimization). We show that in this setting the worst case is reached only for deterministic automata or cover automata following the structure of the de Bruijn words. We refine a previous result by showing that the Berstel/Carton example reported before is actually the absolute worst case time complexity in the case of unary languages for deterministic automata. We show that the same result is valid also when considering the setting of cover automata and an algorithm based on the Hopcroft’s method used for minimization of cover automata. We also show that a LIFO implementation for the splitting list is desirable for the case of unary languages in the setting of deterministic finite automata.

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Author information

Authors and Affiliations

  1. Bioinformatics Department, National Institute of Research and Development for Biological Sciences, Splaiul Independenţei, Nr. 296, Sector 6, Bucharest, Romania

    Andrei Păun

  2. Department of Computer Science, Louisiana Tech University, Ruston, PO Box 10348, Louisiana, LA-71272, USA

    Andrei Păun

  3. Departamento de Inteligencia Artificial, Facultad de Informática, Universidad Politécnica de Madrid, Campus de Montegancedo s/n, Boadilla del Monte, 28660, Madrid, Spain

    Andrei Păun & Alfonso Rodríguez-Patón

  4. Department of Mathematics and Statistics, Louisiana Tech University, Ruston, PO Box 10348, Louisiana, LA-71272, USA

    Mihaela Păun

Authors
  1. Andrei Păun
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  2. Mihaela Păun
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  3. Alfonso Rodríguez-Patón
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Oscar H. Ibarra Bala Ravikumar

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Păun, A., Păun, M., Rodríguez-Patón, A. (2008). Hopcroft’s Minimization Technique: Queues or Stacks?. In: Ibarra, O.H., Ravikumar, B. (eds) Implementation and Applications of Automata. CIAA 2008. Lecture Notes in Computer Science, vol 5148. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70844-5_9

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  • DOI: https://doi.org/10.1007/978-3-540-70844-5_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70843-8

  • Online ISBN: 978-3-540-70844-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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