Bideterministic Automata and Minimal Representations of Regular Languages

  • Hellis Tamm
  • Esko Ukkonen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2759)


Bideterministic automata are deterministic automata with the property of their reversal automata also being deterministic. It has been known that a bideterministic automaton is the minimal deterministic automaton accepting its language. This paper shows that any bideterministic automaton is the unique minimal automaton among all (including nondeterministic) automata accepting the same language. We also present a more general result that shows that under certain conditions a minimal deterministic automaton accepting some language or the reversal of the minimal deterministic automaton of the reversal language is a minimal automaton representation of the language. These conditions can be checked in polynomial time.


Regular Language Minimum Cover Candidate State Minimal Representation Deterministic 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Angluin, D. Inference of reversible languages. Journal of the Association for Computing Machinery 29,3 (1982), 741–765.zbMATHMathSciNetGoogle Scholar
  2. [2]
    Brzozowski, J. A. Canonical regular expressions and minimal state graphs for definite events. In Proceedings of the Symposium on Mathematical Theory of Automata, MRI Symposia Series, vol. 12, Polytechnic Press, Polytechnic Institute of Brooklyn, N.Y., 1963, 529–561.MathSciNetGoogle Scholar
  3. [3]
    Hopcroft, J. E., and Ullman, J.D. Introduction to Automata Theory, Languages, and Computation. Addison-Wesley 1979.Google Scholar
  4. [4]
    Jiang, T., and Ravikumar, B. Minimal NFA problems are hard. SIAM J. Comput. 22,6 (1993), 1117–1141.zbMATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    Kameda, T., and Weiner, P. On the state minimization of nondeterministic automata. IEEE Trans. Comput. C-19,7 (1970), 617–627.CrossRefMathSciNetGoogle Scholar
  6. [6]
    Muder, D. J. Minimal trellises for block codes. IEEE Trans. Inform. Theory 34,5 (1988), 1049–1053.CrossRefMathSciNetGoogle Scholar
  7. [7]
    Pin, J.-E. On reversible automata. In Proceedings of the first LATIN conference, Lecture Notes in Computer Science 583, Springer, 1992, 401–416.Google Scholar
  8. [8]
    Shankar, P., Dasgupta, A., Deshmukh K., and Rajan B. S. On viewing block codes as finite automata. Theoretical Computer Science, 290,3 (2003), 1775–1797.zbMATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    Watson, B. W. Taxonomies and toolkits of regular language algorithms. PhD dissertation, Faculty of Mathematics and Computing Science, Eindhoven University of Technology, Eindhoven, The Netherlands, 1995.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Hellis Tamm
    • 1
  • Esko Ukkonen
    • 1
  1. 1.Department of Computer ScienceUniversity of HelsinkiFinland

Personalised recommendations