Strong Splitting Bisimulation Equivalence

  • J. A. Bergstra
  • C. A. Middelburg
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3629)


We present ACP c , a process algebra with conditional expressions in which the conditions are taken from a Boolean algebra, and extensions of this process algebra with mechanisms for condition evaluation. We confine ourselves to finitely branching processes. This restriction makes it possible to present c in a concise and intuitively clear way, and to bring the notion of splitting bisimulation equivalence and the issue of condition evaluation in process algebras with conditional expressions to the forefront.


Condition Evaluation Boolean Algebra Composition Operator Transition Rule Process Algebra 
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  1. 1.
    Bergstra, J.A., Klop, J.W.: Process algebra for synchronous communication. Information and Control 60, 109–137 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Baeten, J.C.M., Weijland, W.P.: Process Algebra. Cambridge Tracts in Theoretical Computer Science, vol. 18. Cambridge University Press, Cambridge (1990)CrossRefGoogle Scholar
  3. 3.
    Baeten, J.C.M., Bergstra, J.A., Mauw, S., Veltink, G.J.: A process specification formalism based on static COLD. In: Bergstra, J.A., Feijs, L.M.G. (eds.) Algebraic Methods 1989. LNCS, vol. 490, pp. 303–335. Springer, Heidelberg (1991)Google Scholar
  4. 4.
    Baeten, J.C.M., Bergstra, J.A.: Process algebra with signals and conditions. In: Broy, M. (ed.) Programming and Mathematical Methods. NATO ASI Series, vol. F88, pp. 273–323. Springer, Heidelberg (1992)Google Scholar
  5. 5.
    Bergstra, J.A., Ponse, A., van Wamel, J.J.: Process algebra with backtracking. In: de Bakker, J.W., de Roever, W.P., Rozenberg, G. (eds.) REX 1993. LNCS, vol. 803, pp. 46–91. Springer, Heidelberg (1994)Google Scholar
  6. 6.
    Baeten, J.C.M., Bergstra, J.A.: Process algebra with propositional signals. Theoretical Computer Science 177, 381–405 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Hennessy, M., Milner, R.: Algebraic laws for non-determinism and concurrency. Journal of the ACM 32, 137–161 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Brookes, S.D., Hoare, C.A.R., Roscoe, A.W.: A theory of communicating sequential processes. Journal of the ACM 31, 560–599 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Bergstra, J.A., Ponse, A.: Process algebra and conditional composition. Information Processing Letters 80, 41–49 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    van der Zwaag, M.B.: Models and Logics for Process Algebra. PhD thesis, Programming Research Group, University of Amsterdam, Amsterdam (2002)Google Scholar
  11. 11.
    Bergstra, J.A., Middelburg, C.A.: Splitting bisimulations and retrospective conditions. Computer Science Report 05-03, Department of Mathematics and Computer Science, Eindhoven University of Technology (2005)Google Scholar
  12. 12.
    Monk, J.D., Bonnet, R. (eds.): Handbook of Boolean Algebras, vol. 1. Elsevier, Amsterdam (1989)zbMATHGoogle Scholar
  13. 13.
    Hoare, C.A.R., Hayes, I.J., Jifeng, H., Morgan, C.C., Roscoe, A.W., Sanders, J.W., Sorensen, I.H., Spivey, J.M., Sufrin, B.A.: Laws of programming. Communications of the ACM 30, 672–686 (1987)zbMATHCrossRefGoogle Scholar
  14. 14.
    Halmos, P.R.: Lectures on Boolean Algebras. Mathematical Studies, Van Nostrand, Princeton, NJ (1963)Google Scholar
  15. 15.
    Busi, N., van Glabbeek, R.J., Gorrieri, R.: Axiomatising ST-bisimulation semantics. In: Olderog, R.R. (ed.) PROCOMET 1994. IFIP Transactions A, vol. 56, pp. 169–188. North-Holland, Amsterdam (1994)Google Scholar
  16. 16.
    Baeten, J.C.M., Verhoef, C.: Concrete process algebra. In: Abramsky, S., Gabbay, D.M., Maibaum, T.S.E. (eds.) Handbook of Logic in Computer Science, vol. IV, pp. 149–268. Oxford University Press, Oxford (1995)Google Scholar
  17. 17.
    Groote, J.F., Ponse, A.: Proof theory for μCRL: A language for processes with data. In: Andrews, D.J., Groote, J.F., Middelburg, C.A. (eds.) Semantics of Specification Languages. Workshops in Computing Series, pp. 232–251. Springer, Heidelberg (1994)Google Scholar
  18. 18.
    Baeten, J.C.M., Bergstra, J.A.: Global renaming operators in concrete process algebra. Information and Control 78, 205–245 (1988)zbMATHMathSciNetGoogle Scholar
  19. 19.
    Groote, J.F., Ponse, A.: The syntax and semantics of μCRL. In: Ponse, A., Verhoef, C., van Vlijmen, S.F.M. (eds.) Algebra of Communicating Processes. Workshops in Computing Series, pp. 26–62. Springer, Heidelberg (1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • J. A. Bergstra
    • 1
    • 2
  • C. A. Middelburg
    • 3
  1. 1.Programming Research GroupUniversity of AmsterdamAmsterdamThe Netherlands
  2. 2.Department of PhilosophyUtrecht UniversityUtrechtThe Netherlands
  3. 3.Computing Science DepartmentEindhoven University of TechnologyEindhovenThe Netherlands

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