Hopcroft's Minimization Technique: Queues or Stacks?

  • Authors:

  • Andrei Păun;Mihaela Păun;Alfonso Rodríguez-Patón

  • Affiliations:

  • Bioinformatics Department, National Institute of Research and Development for Biological Sciences, Bucharest, Romania and Department of Computer Science, Louisiana Tech University, Ruston, Louisia ...;Department of Mathematics and Statistics, Louisiana Tech University, Ruston, Louisiana, USA LA-71272;Departamento de Inteligencia Artificial, Facultad de Informática, Universidad Politécnica de Madrid, Madrid, Spain 28660

  • Venue:
  • CIAA '08 Proceedings of the 13th international conference on Implementation and Applications of Automata
  • Year:
  • 2008

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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.