Faster Algorithm for Bisimulation Equivalence of Normed Context-Free Processes

  • Sławomir Lasota
  • Wojciech Rytter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4162)


The fastest known algorithm for checking bisimulation equivalence of normed context-free processes worked in O(n13) 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 \(O(n^6 {\sl polylog} n)\).


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  1. 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)MATHMathSciNetGoogle Scholar
  2. 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)CrossRefGoogle Scholar
  3. 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. 4.
    Caucal, D.: Graphes canoniques des graphes algébraiques. Informatique Théoretique et Applications (RAIRO) 24(4), 339–352 (1990)MATHMathSciNetGoogle Scholar
  5. 5.
    Christensen, S., Hirshfeld, Y., Stirling, C.: Bisimulation equivalence is decidable for all context-free processes. Information and Computation 12(2), 143–148 (1995)CrossRefGoogle Scholar
  6. 6.
    Friedman, E.P.: The inclusion problem for simple languages. Theoretical Computer Science 1, 297–316 (1976)MATHCrossRefGoogle Scholar
  7. 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. 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. 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)CrossRefMathSciNetGoogle Scholar
  10. 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. 11.
    Huynh, D., Tian, L.: Deciding bisimilarity of normed context-free processes is in \(\sum^P_2\). Theoretical Computer Science 123, 183–197 (1994)MATHCrossRefMathSciNetGoogle Scholar
  12. 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. 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)CrossRefGoogle Scholar
  14. 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)MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Sławomir Lasota
    • 1
  • Wojciech Rytter
    • 1
  1. 1.Institute of InformaticsWarsaw UniversityWarsawPoland

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