Directly Constructing Minimal DFAs: Combining Two Algorithms by Brzozowski

  • Bruce W. Watson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2088)


In this paper, we combine (and refine) two of Brzozowski’s algorithms — yielding a single algorithm which constructs a minimal deterministic finite automaton (DFA) from a regular expression.


Regular Expression Minimization Algorithm Construction Algorithm Incremental Algorithm Finite State Automaton 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Brzozowski, J.A. Canonical regular expressions and minimal state graphs for definite events, in: Mathematical Theory of Automata. (pp. 529–561, Vol. 12, MRI Symposia Series, Polytechnic Press, Polytechnic Institute of Brooklyn, NY, 1962).Google Scholar
  2. 2.
    Brzozowski, J.A. Derivatives of regular expressions. (J. ACM 11(4), pp. 481–494, 1964).zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Daciuk, J.D., Watson, B.W. and R.E. Watson. An Incremental Algorithm for Constructing Acyclic Deterministic Transducers. (Proceedings of the International Workshop on Finite State Methods in Natural Language Processing, Ankara, Turkey, 30 June-1 July 1998).Google Scholar
  4. 4.
    Daciuk, J.D., Mihov, S., Watson, B.W. and R.E. Watson. Incremental Construction of Minimal Acyclic Finite State Automata. (to appear in Computational Linguistics, 2000).Google Scholar
  5. 5.
    Dijkstra, E.W. A Discipline of Programming. (Prentice Hall, Englewood Cliffs, N.J., 1976).zbMATHGoogle Scholar
  6. 6.
    Gries, D. Describing an Algorithm by Hopcroft. (Acta Informatica 2, pp. 97–109, 1973).zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Hopcroft, J.E. and J.D. Ullman. Introduction to Automata, Theory, Languages and Computation. (Addison-Wesley, Reading, M.A., 1979).zbMATHGoogle Scholar
  8. 8.
    Mihov, S. Direct Building of Minimal Automaton for Given List. (Available from Scholar
  9. 9.
    Revuz, D. Minimisation of Acyclic Deterministic Automata in Linear Time. (Theoretical Computer Science 92, pp. 181–189, 1992).zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Watson, B.W. Taxonomies and Toolkits of Regular Language Algorithms. (Ph.D dissertation, Eindhoven University of Technology, The Netherlands, 1995). See
  11. 11.
    Watson, B.W. A Fast New Semi-Incremental Algorithm for the Construction of Minimal Acyclic DFAs. (Proceedings of the Third Workshop on Implementing Automata, Rouen, France, September 1998).Google Scholar
  12. 12.
    Watson, B.W. A History of Brzozowski’s DFA minimization algorithm. (Poster at the International Conference on Implementing Automata, London, Ontario, 2000).Google Scholar
  13. 13.
    Watson, B.W. A New Recursive Incremental Algorithm for Building Minimal Acyclic Deterministic Finite Automata. (to appear, 2000).Google Scholar
  14. 14.
    Wood, D. Theory of Computation. (Harper & Row, New York, N.Y., 1987).zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Bruce W. Watson
    • 1
  1. 1.(Department of Computer Science)University of PretoriaPretoriaSouth Africa

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