A Finite Equational Base for CCS with Left Merge and Communication Merge | SpringerLink
Skip to main content

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

  • Conference paper
Automata, Languages and Programming (ICALP 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4052))

Included in the following conference series:

Abstract

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.

The first and third author were partly supported by the project “The Equational Logic of Parallel Processes” (nr. 060013021) of The Icelandic Research Fund.

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. 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)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Chapter  Google Scholar 

  3. Bergstra, J.A., Klop, J.W.: Process algebra for synchronous communication. Inform. and Control 60(1-3), 109–137 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bergstra, J.A., Tucker, J.V.: Top-down design and the algebra of communicating processes. Sci. Comput. Programming 5(2), 171–199 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  5. de Simone, R.: Higher-level synchronising devices in Meije-SCCS. Theor. Comput. Sci. 37, 245–267 (1985)

    Article  MATH  Google Scholar 

  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. Heering, J.: Partial evaluation and ω-completeness of algebraic specifications. Theoret. Comput. Sci. 43(2-3), 149–167 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  8. Hennessy, M.: Axiomatising finite concurrent processes. SIAM J. Comput. 17(5), 997–1017 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  9. Hennessy, M., Milner, R.: Algebraic laws for nondeterminism and concurrency. J. ACM 32(1), 137–161,(January 1985)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  11. Milner, R.: Communication and Concurrency. Prentice-Hall, Englewood Cliffs (1989)

    MATH  Google Scholar 

  12. Moller, F.: Axioms for Concurrency. PhD thesis, University of Edinburgh (1989)

    Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  15. Taylor, W.: Equational logic. Houston J. Math (Survey) (1979)

    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

Aceto, L., Fokkink, W., Ingolfsdottir, A., Luttik, B. (2006). A Finite Equational Base for CCS with Left Merge and Communication Merge. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds) Automata, Languages and Programming. ICALP 2006. Lecture Notes in Computer Science, vol 4052. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11787006_42

Download citation

  • DOI: https://doi.org/10.1007/11787006_42

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35907-4

  • Online ISBN: 978-3-540-35908-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics