Hopcroft’s Minimization Technique: Queues or Stacks?

  • Andrei Păun
  • Mihaela Păun
  • Alfonso Rodríguez-Patón
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5148)


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.


Regular Language Splitting Sequence Deterministic Finite Automaton Deterministic Automaton Unary Language 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Andrei Păun
    • 1
    • 2
    • 3
  • Mihaela Păun
    • 4
  • Alfonso Rodríguez-Patón
    • 3
  1. 1.Bioinformatics DepartmentNational Institute of Research and Development for Biological SciencesBucharestRomania
  2. 2.Department of Computer ScienceLouisiana Tech University, RustonLouisianaUSA
  3. 3.Departamento de Inteligencia Artificial, Facultad de InformáticaUniversidad Politécnica de MadridMadridSpain
  4. 4.Department of Mathematics and StatisticsLouisiana Tech University, RustonLouisianaUSA

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