Skip to main content
SpringerLink
Log in

Short Regular Expressions from Finite Automata: Empirical Results

  • Conference paper
Implementation and Application of Automata (CIAA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5642))

Included in the following conference series:

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Almeida, M., Moreira, N., Reis, R.: Enumeration and generation with a string automata representation. Theor. Comput. Sci. 387(2), 93–102 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  3. Edwards, K., Farr, G.E.: Planarization and fragmentability of some classes of graphs. Discrete Math. 308(12), 2396–2406 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. Eggan, L.C.: Transition graphs and the star height of regular events. Mich. Math. J. 10, 385–397 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  5. Ehrenfeucht, A., Zeiger, H.P.: Complexity measures for regular expressions. J. Comput. Syst. Sci. 12(2), 134–146 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    MathSciNet  MATH  Google Scholar 

  7. Feige, U., Hajiaghayi, M., Lee, J.R.: Improved approximation algorithms for minimum weight vertex separators. SIAM J. Comput. 38(2), 629–657 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  13. Han, Y., Wood, D.: Obtaining shorter regular expressions from finite-state automata. Theor. Comput. Sci. 370(1-3), 110–120 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  14. Hopcroft, J.E., Ullman, J.D.: Introduction to automata theory, languages and computation. Addison-Wesley, Reading (1979)

    MATH  Google Scholar 

  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. Le Maout, V.: Cursors. In: Yu, S., Păun, A. (eds.) CIAA 2000. LNCS, vol. 2088, pp. 195–207. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  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. Ponty, Y., Termier, M., Denise, A.: GenRGenS: software for generating random genomic sequences and structures. Bioinformatics 22(12), 1534–1535 (2006)

    Article  Google Scholar 

  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)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Giessen, Arndtstraße 2, D-35392, Giessen, Germany

    Hermann Gruber & Markus Holzer

  2. Fachbereich Informatik, Technische Universität Darmstadt, Hochschulstraße 10, D-64289, Darmstadt, Germany

    Michael Tautschnig

Authors
  1. Hermann Gruber
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Markus Holzer
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michael Tautschnig
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. NICTA and University of New South Wales, Sydney, Australia

    Sebastian Maneth

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gruber, H., Holzer, M., Tautschnig, M. (2009). Short Regular Expressions from Finite Automata: Empirical Results. In: Maneth, S. (eds) Implementation and Application of Automata. CIAA 2009. Lecture Notes in Computer Science, vol 5642. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02979-0_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02979-0_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02978-3

  • Online ISBN: 978-3-642-02979-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation