A Finite Equational Base for CCS with Left Merge and Communication Merge

  • Luca Aceto
  • Wan Fokkink
  • Anna Ingolfsdottir
  • Bas Luttik
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4052)


Using the left merge and communication merge from ACP, we present an equational base (i.e., a ground-complete and ω-complete set of valid equations) for the fragment of CCS without restriction and relabelling. Our equational base is finite if the set of actions is finite.


Normal Form Equational Theory Communication Function Parallel Composition Process Algebra 
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  1. 1.
    Aceto, L., Fokkink, W.J., Ingolfsdottir, A., Luttik, B.: CCS with Hennessy’s merge has no finite equational axiomatization. Theor. Comput. Sci. 330(3), 377–405 (2005)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Aceto, L., Fokkink, W.J., Ingólfsdóttir, A., Luttik, B.: Finite Equational Bases in Process Algebra: Results and Open Questions. In: Middeldorp, A., van Oostrom, V., van Raamsdonk, F., de Vrijer, R. (eds.) Processes, Terms and Cycles: Steps on the Road to Infinity. LNCS, vol. 3838, pp. 338–367. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  3. 3.
    Bergstra, J.A., Klop, J.W.: Process algebra for synchronous communication. Inform. and Control 60(1-3), 109–137 (1984)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Bergstra, J.A., Tucker, J.V.: Top-down design and the algebra of communicating processes. Sci. Comput. Programming 5(2), 171–199 (1985)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    de Simone, R.: Higher-level synchronising devices in Meije-SCCS. Theor. Comput. Sci. 37, 245–267 (1985)MATHCrossRefGoogle Scholar
  6. 6.
    Groote, J.F.: A new strategy for proving ω-completeness applied to process algebra. In: Baeten, J.C.M., Klop, J.W. (eds.) CONCUR 1990. LNCS, vol. 458, pp. 314–331. Springer, Heidelberg (1990)Google Scholar
  7. 7.
    Heering, J.: Partial evaluation and ω-completeness of algebraic specifications. Theoret. Comput. Sci. 43(2-3), 149–167 (1986)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Hennessy, M.: Axiomatising finite concurrent processes. SIAM J. Comput. 17(5), 997–1017 (1988)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Hennessy, M., Milner, R.: Algebraic laws for nondeterminism and concurrency. J. ACM 32(1), 137–161,(January 1985)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Luttik, B., van Oostrom, V.: Decomposition orders—another proof of the fundamental theorem of arithmetic. Theor. Comput. Sci. 335(2–3), 147–186 (2005)MATHCrossRefGoogle Scholar
  11. 11.
    Milner, R.: Communication and Concurrency. Prentice-Hall, Englewood Cliffs (1989)MATHGoogle Scholar
  12. 12.
    Moller, F.: Axioms for Concurrency. PhD thesis, University of Edinburgh (1989)Google Scholar
  13. 13.
    Moller, F.: The nonexistence of finite axiomatisations for CCS congruences. In: Proceedings of LICS1990, pp. 142–153. IEEE Computer Society Press, Los Alamitos (1990)Google Scholar
  14. 14.
    Park, D.M.R.: Concurrency and automata on infinite sequences. In: Deussen, P. (ed.) GI-TCS 1981. LNCS, vol. 104, pp. 167–183. Springer, Heidelberg (1981)CrossRefGoogle Scholar
  15. 15.
    Taylor, W.: Equational logic. Houston J. Math (Survey) (1979)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Luca Aceto
    • 1
    • 4
  • Wan Fokkink
    • 2
    • 5
  • Anna Ingolfsdottir
    • 1
    • 4
  • Bas Luttik
    • 3
    • 5
  1. 1.Department of Computer ScienceReykjavík UniversityIceland
  2. 2.Department of Computer ScienceVrije Universiteit AmsterdamThe Netherlands
  3. 3.Department of Mathematics and Computer ScienceTechnische Universiteit EindhovenThe Netherlands
  4. 4.BRICS, Department of Computer ScienceAalborg UniversityDenmark
  5. 5.Department of Software EngineeringCWIThe Netherlands

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