How to use sorting procedures to minimize DFA

  • Barbara Schubert
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1260)


In this paper we introduce a new idea, which can be used in minimization of a deterministic finite automaton. Namely, we associate names with states of an automaton and we sort them. We give a new algorithm, its correctness proof, and its proof of execution time bound. This algorithm has time complexity O(n2 log n) and can be considered as a direct improvement of Wood's algorithm [6] which has time complexity O(n3), where n is the number of states. Wood's algorithm checks if pairs of states are distinguishable. It is improved by making better use of transitivity. Similarly some other algorithms which check if pairs of states are distinguishable can be improved using sorting procedures.


Equivalence Class Time Complexity Reachable State Correctness Proof Transition List 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Barbara Schubert
    • 1
  1. 1.Department of Computer ScienceThe University of Western OntarioLondonCanada

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