Thompson Digraphs: A Characterization

  • Dora Giammarresi
  • Jean-Luc Ponty
  • Derick Wood
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2214)


A finite-state machine is called a Thompson machine if it can be constructed from a regular expression using Thompson’s construction. We call the underlying digraph of a Thompson machine a Thompson digraph. We establish and prove a characterization of Thompson digraphs. As one application of the characterization, we give an algorithm that generates an equivalent regular expression from a Thompson machine in time linear in the number of states.


Time Linear Regular Expression Expression Tree Back Edge Source Vertex 
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  1. 1.
    A.V. Aho and J.D. Ullman. The Theory of Parsing, Translation, and Compiling, Vol. I: Parsing. Prentice-Hall, Inc., Englewood Cliffs, NJ, 1972.Google Scholar
  2. 2.
    A. Bruggemann-Klein and D. Wood. The validation of SGML content models. Mathematical and Computer Modelling, 25:73–84, 1997.CrossRefGoogle Scholar
  3. 3.
    P. Caron and D. Ziadi. Characterization of Glushkov automata. Theoretical Computer Science, 1998. To appear.Google Scholar
  4. 4.
    D. Giammarresi, J.-L Ponty, and D. Wood. The Glushkov and Thompson constructions: A synthesis. Unpublished manuscript, July 1998. URL:
  5. 5.
    D. Giammarresi, J.-L Ponty, and D. Wood. A characterization of Thompson digraphs. Unpublished manuscript, January 1999. URL:
  6. 6.
    B. G. Mirkin. An algorithm for constructing a base in a language of regular expressions. Engineering Cybernetics, 5:110–116, 1966.Google Scholar
  7. 7.
    S. Sippu and E. Soisalon-Soininen. Parsing Theory: I Languages and Parsing. EATCS Monographs on Theoretical Computer Science, Volume 15. Springer-Verlag, New York, NY, 1988.Google Scholar
  8. 8.
    K. Thompson. Regular expression search algorithm. Communications of the ACM, 11:419–422, 1968.zbMATHCrossRefGoogle Scholar
  9. 9.
    D. Wood. Theory of Computation. John Wiley & Sons, Inc., New York, NY, second edition, 1998. In preparation.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Dora Giammarresi
    • 1
  • Jean-Luc Ponty
    • 2
  • Derick Wood
    • 3
  1. 1.Dipartimento di Matematica Applicata e InformaticaUniversit`a Ca’ Foscari di VeneziaVenezia MestreItaly
  2. 2.L.I.F.A.R.Université de Rouen, Faculté des Sciences et des TechniquesMont-Saint-Aignan CedexFrance
  3. 3.Department of Computer ScienceHong Kong University of Science & TechnologyKowloonHong Kong

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