Advertisement

A Context-Free Process as a Pushdown Automaton

  • J. C. M. Baeten
  • P. J. L. Cuijpers
  • P. J. A. van Tilburg
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5201)

Abstract

A well-known theorem in automata theory states that every context-free language is accepted by a pushdown automaton. We investigate this theorem in the setting of processes, using the rooted branching bisimulation and contrasimulation equivalences instead of language equivalence. In process theory, different from automata theory, interaction is explicit, so we realize a pushdown automaton as a regular process communicating with a stack.

Keywords

Transition System Equational Theory Regular Language Sequential Composition Operational Rule 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aceto, L., Fokkink, W.J., Verhoef, C.: Structural operational semantics. In: Bergstra, J., Ponse, A., Smolka, S. (eds.) Handbook of Process Algebra, pp. 197–292. North-Holland, Amsterdam (2001)CrossRefGoogle Scholar
  2. 2.
    Baeten, J.C.M., Basten, T., Reniers, M.A.: Process Algebra: Equational Theories of Communicating Processes. Cambridge University Press, Cambridge (2008)Google Scholar
  3. 3.
    Baeten, J.C.M., Bergstra, J.A., Klop, J.W.: On the consistency of Koomen’s fair abstraction rule. Theoretical Computer Science 51(1–2), 129–176 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Baeten, J.C.M., Bergstra, J.A., Klop, J.W.: Decidability of bisimulation equivalence for processes generating context-free languages. Journal of the ACM 40(3), 653–682 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Baeten, J.C.M., Bravetti, M.: A ground-complete axiomatization of finite state processes in process algebra. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 246–262. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Baeten, J.C.M., Weijland, W.P.: Process Algebra. Cambridge University Press, Cambridge (1990)Google Scholar
  7. 7.
    Bergstra, J.A., Klop, J.W.: Process algebra for synchronous communication. Information and Control 60(1/3), 109–137 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Bosscher, D.J.B.: Grammars modulo bisimulation. Ph.D. thesis. University of Amsterdam (1997)Google Scholar
  9. 9.
    Caucal, D.: Branching bisimulation for context-free processes. In: Shyamasundar, R.K. (ed.) FSTTCS 1992. LNCS, vol. 652, pp. 316–327. Springer, Heidelberg (1992)Google Scholar
  10. 10.
    Christensen, S., Hirshfeld, Y., Moller, F.: Bisimulation equivalence is decidable for basic parallel processes. In: Best, E. (ed.) CONCUR 1993. LNCS, vol. 715, pp. 143–157. Springer, Heidelberg (1993)Google Scholar
  11. 11.
    Christensen, S., Hüttel, H., Stirling, C.: Bisimulation equivalence is decidable for all context-free processes. In: Cleaveland, W.R. (ed.) CONCUR 1992. LNCS, vol. 630, pp. 138–147. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  12. 12.
    van Glabbeek, R.J.: The linear time – branching time spectrum ii. In: Best, E. (ed.) CONCUR 1993. LNCS, vol. 715, pp. 66–81. Springer, Heidelberg (1993)Google Scholar
  13. 13.
    van Glabbeek, R.J., Weijland, W.P.: Branching time and abstraction in bisimulation semantics. Journal of the ACM 43(3), 555–600 (1996)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Groote, J.F., Reniers, M.A.: Algebraic process verification. In: Bergstra, J., Ponse, A., Smolka, S. (eds.) Handbook of Process Algebra, pp. 1151–1208. North-Holland, Amsterdam (2001)CrossRefGoogle Scholar
  15. 15.
    Luttik, B.: Choice quantification in process algebra, Ph.D. thesis. University of Amsterdam (2002)Google Scholar
  16. 16.
    Moller, F.: The importance of the left merge operator in process algebras. In: Paterson, M. (ed.) ICALP 1990. LNCS, vol. 443, pp. 752–764. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  17. 17.
    Moller, F.: Infinite results. In: Sassone, V., Montanari, U. (eds.) CONCUR 1996. LNCS, vol. 1119, pp. 195–216. Springer, Heidelberg (1996)Google Scholar
  18. 18.
    Srba, J.: Deadlocking states in context-free process algebra. In: Brim, L., Gruska, J., Zlatuska, J. (eds.) MFSC 1998. LNCS, vol. 1450, pp. 388–398. Springer, Heidelberg (1998)Google Scholar
  19. 19.
    Voorhoeve, M., Mauw, S.: Impossible futures and determinism. Information Processing Letters 80(1), 51–58 (2001)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • J. C. M. Baeten
    • 1
  • P. J. L. Cuijpers
    • 1
  • P. J. A. van Tilburg
    • 1
  1. 1.Division of Computer ScienceEindhoven University of TechnologyEindhovenThe Netherlands

Personalised recommendations