Short Regular Expressions from Finite Automata: Empirical Results

  • Hermann Gruber
  • Markus Holzer
  • Michael Tautschnig
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5642)


We continue our work [H. Gruber, M. Holzer: Provably shorter regular expressions from deterministic finite automata (extended abstract). In Proc. DLT, LNCS 5257, 2008] on the problem of finding good elimination orderings for the state elimination algorithm, one of the most popular algorithms for the conversion of finite automata into equivalent regular expressions. Here we tackle this problem both from the theoretical and from the practical side. First we show that the problem of finding optimal elimination orderings can be used to estimate the cycle rank of the underlying automata. This gives good evidence that the problem under consideration is difficult, to a certain extent. Moreover, we conduct experiments on a large set of carefully chosen instances for five different strategies to choose elimination orderings, which are known from the literature. Perhaps the most surprising result is that a simple greedy heuristic by [M. Delgado, J. Morais: Approximation to the smallest regular expression for a given regular language. In Proc. CIAA, LNCS 3317, 2004] almost always outperforms all other strategies, including those with a provable performance guarantee.


Regular Expression Regular Language Finite Automaton Elimination Ordering Input Alphabet 
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.
    Almeida, M., Moreira, N., Reis, R.: Enumeration and generation with a string automata representation. Theor. Comput. Sci. 387(2), 93–102 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Delgado, M., Morais, J.: Approximation to the smallest regular expression for a given regular language. In: Domaratzki, M., Okhotin, A., Salomaa, K., Yu, S. (eds.) CIAA 2004. LNCS, vol. 3317, pp. 312–314. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  3. 3.
    Edwards, K., Farr, G.E.: Planarization and fragmentability of some classes of graphs. Discrete Math. 308(12), 2396–2406 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Eggan, L.C.: Transition graphs and the star height of regular events. Mich. Math. J. 10, 385–397 (1963)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Ehrenfeucht, A., Zeiger, H.P.: Complexity measures for regular expressions. J. Comput. Syst. Sci. 12(2), 134–146 (1976)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Ellul, K., Krawetz, B., Shallit, J., Wang, M.: Regular expressions: New results and open problems. J. Autom. Lang. Comb. 10(4), 407–437 (2005)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Feige, U., Hajiaghayi, M., Lee, J.R.: Improved approximation algorithms for minimum weight vertex separators. SIAM J. Comput. 38(2), 629–657 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Frishert, M., Cleophas, L.G., Watson, B.W.: The effect of rewriting regular expressions on their accepting automata. In: Ibarra, O.H., Dang, Z. (eds.) CIAA 2003, vol. 2759, pp. 304–305. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  9. 9.
    Gelade, W., Neven, F.: Succinctness of the complement and intersection of regular expressions. In: STACS 2008. Dagstuhl Seminar Proceedings, vol. 08001, pp. 325–336. IBFI Schloss Dagstuhl (2008)Google Scholar
  10. 10.
    Gruber, H., Holzer, M.: Finite automata, digraph connectivity, and regular expression size. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 39–50. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  11. 11.
    Gruber, H., Holzer, M.: Provably shorter regular expressions from deterministic finite automata (extended abstract). In: Ito, M., Toyama, M. (eds.) DLT 2008. LNCS, vol. 5257, pp. 383–395. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    Gruber, H., Johannsen, J.: Optimal lower bounds on regular expression size using communication complexity. In: Amadio, R.M. (ed.) FOSSACS 2008. LNCS, vol. 4962, pp. 273–286. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  13. 13.
    Han, Y., Wood, D.: Obtaining shorter regular expressions from finite-state automata. Theor. Comput. Sci. 370(1-3), 110–120 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Hopcroft, J.E., Ullman, J.D.: Introduction to automata theory, languages and computation. Addison-Wesley, Reading (1979)zbMATHGoogle Scholar
  15. 15.
    Kleene, S.C.: Representation of events in nerve nets and finite automata. In: Automata studies, pp. 3–42. Princeton University Press, Princeton (1956)Google Scholar
  16. 16.
    Le Maout, V.: Cursors. In: Yu, S., Păun, A. (eds.) CIAA 2000. LNCS, vol. 2088, pp. 195–207. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  17. 17.
    Morgan, K.: Approximation algorithms for the maximum induced planar and outerplanar subgraph problems. Bachelor with honors thesis, Monash University, Australia (2005)Google Scholar
  18. 18.
    Ponty, Y., Termier, M., Denise, A.: GenRGenS: software for generating random genomic sequences and structures. Bioinformatics 22(12), 1534–1535 (2006)CrossRefGoogle Scholar
  19. 19.
    Sakarovitch, J.: The language, the expression, and the (small) automaton. In: Farré, J., Litovsky, I., Schmitz, S. (eds.) CIAA 2005. LNCS, vol. 3845, pp. 15–30. Springer, Heidelberg (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Hermann Gruber
    • 1
  • Markus Holzer
    • 1
  • Michael Tautschnig
    • 2
  1. 1.Institut für InformatikUniversität GiessenGiessenGermany
  2. 2.Fachbereich InformatikTechnische Universität DarmstadtDarmstadtGermany

Personalised recommendations