Skip to main content

Faster Algorithm for Bisimulation Equivalence of Normed Context-Free Processes

  • Conference paper
Mathematical Foundations of Computer Science 2006 (MFCS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4162))

  • 1069 Accesses

Abstract

The fastest known algorithm for checking bisimulation equivalence of normed context-free processes worked in O(n 13) time. We give an alternative algorithm working in \(O(n^8 {\sl polylog} n)\) time, As a side effect we improve the best known upper bound for testing equivalence of simple context-free grammars from \(O(n^7 {\sl polylog} n)\) to \(O(n^6 {\sl polylog} n)\).

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Bar-Hillel, Y., Perles, M., Shamir, S.: On formal properties of simple phrase structure grammars. Zeitschrift fuer Phonetik, Sprachwissenschaft, und Kommunikationsforschung 14, 143–177 (1961)

    MATH  MathSciNet  Google Scholar 

  2. Bastien, C., Czyzowicz, J., Fraczak, W., Rytter, W.: Prime normal form and equivalence of simple grammars. In: Farré, J., Litovsky, I., Schmitz, S. (eds.) CIAA 2005. LNCS, vol. 3845, pp. 78–89. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  3. Beaten, J., Bergstra, J., Klop, J.: Decidability of bisimulation equivalence for processes generating context-free languages. In: de Bakker, J.W., Nijman, A.J., Treleaven, P.C. (eds.) PARLE 1987. LNCS, vol. 259, pp. 94–113. Springer, Heidelberg (1987)

    Google Scholar 

  4. Caucal, D.: Graphes canoniques des graphes algébraiques. Informatique Théoretique et Applications (RAIRO) 24(4), 339–352 (1990)

    MATH  MathSciNet  Google Scholar 

  5. Christensen, S., Hirshfeld, Y., Stirling, C.: Bisimulation equivalence is decidable for all context-free processes. Information and Computation 12(2), 143–148 (1995)

    Article  Google Scholar 

  6. Friedman, E.P.: The inclusion problem for simple languages. Theoretical Computer Science 1, 297–316 (1976)

    Article  MATH  Google Scholar 

  7. Glabbeek, R.v.: The linear time - branching time spectrum. In: Baeten, J.C.M., Klop, J.W. (eds.) CONCUR 1990. LNCS, vol. 458, pp. 278–297. Springer, Heidelberg (1990)

    Google Scholar 

  8. Groote, J., Keinänen, M.: A Sub-quadratic Algorithm for Conjunctive and Disjunctive BESs. CS-Report 04-13, Department of Mathematics and Computer Science, Technische Universiteit Eindhoven (June 2004)

    Google Scholar 

  9. Hirshfeld, Y., Jerrum, M., Moller, F.: A polynomial algorithm for deciding bisimilarity on normed context-free processes. Theoretical Computer Science 15, 143–159 (1996)

    Article  MathSciNet  Google Scholar 

  10. Huettel, H., Stirling, C.: Actions speak louder than words: proving bisimilarity for context-free processes. In: Proc. LICS 1991, pp. 376–386. IEEE Computer Society Press, Los Alamitos (1991)

    Google Scholar 

  11. Huynh, D., Tian, L.: Deciding bisimilarity of normed context-free processes is in \(\sum^P_2\). Theoretical Computer Science 123, 183–197 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  12. Korenjak, A., Hopcroft, J.: Simple deterministic languages. In: Proc. 7th Annual IEEE Symposium on Switching and Automata Theory, pp. 36–46 (1966)

    Google Scholar 

  13. Plandowski, W.: Testing equivalence of morphisms on context-free languages. In: van Leeuwen, J. (ed.) ESA 1994. LNCS, vol. 855, pp. 460–470. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  14. Shinohara, A., Miyazaki, M., Takeda, M.: An improved pattern-matching for strings in terms of straight-line programs. Journal of Discrete Algorithms 1(1), 187–204 (2000)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lasota, S., Rytter, W. (2006). Faster Algorithm for Bisimulation Equivalence of Normed Context-Free Processes. In: Královič, R., Urzyczyn, P. (eds) Mathematical Foundations of Computer Science 2006. MFCS 2006. Lecture Notes in Computer Science, vol 4162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11821069_56

Download citation

  • DOI: https://doi.org/10.1007/11821069_56

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-37791-7

  • Online ISBN: 978-3-540-37793-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics