Abstract
In this paper, we examine equational axiomatisations for PA, the process algebra of Bergstra and Klop, which is a simple subset of their full language ACP. The language PA has two combinators for concurrent execution: the usual full merge operator ∥ and the more esoteric left merge operator ⌊. Though this latter combinator is somewhat semantically unusual, we demonstrate its importance by proving that, whereas a finite sound and complete equational theory exists for PA, no such finite theory can exist for PA in the absence of the left merge operator.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Bibliography
J.A. Bergstra, J.W. Klop, “Process Algebra for Synchronous Communication”, Information and Computation, Vol 60, No 1/3, 1984.
J.A. Bergstra, J.W. Klop, “Algebra of Communicating Processes with Abstraction”, Theoretical Computer Science, Vol 37, No 1, 1985.
G. Boudol, I. Castellani, “On the Semantics of Concurrency: Partial Orders and Transition Systems”, Proc. TAPSOFT '87, Vol I, LNCS 249, Springer-Verlag, 1987.
M. Hennessy, “Axiomatising Finite Concurrent Processes”, University of Sussex Computer Science Department Report No 4/87, July 1987.
R. Milner, A Calculus of Communicating Systems, LNCS 92, Springer-Verlag, 1980.
R. Milner, Communication and Concurrency, Prentice-Hall International, 1989.
R. Milner, F. Moller, “Unique Decomposition of Processes”, Bulletin of the EATCS, 1990 (to appear).
F. Moller, “Axioms for Concurrency”, Ph.D. Thesis, University of Edinburgh, Report No ECS-LFCS-89-84, 1989.
F. Moller, “The Nonexistence of Finite Axiomatisations for CCS Congruences”, Proceedings LICS90, 1990.
D.M.R. Park, “Concurrency and Automata on Infinite Sequences”, Proceedings of the 5th G.I. Conference, Lecture Notes in Computer Science 104, Springer-Verlag, 1981.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1990 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Moller, F. (1990). The importance of the left merge operator in process algebras. In: Paterson, M.S. (eds) Automata, Languages and Programming. ICALP 1990. Lecture Notes in Computer Science, vol 443. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0032072
Download citation
DOI: https://doi.org/10.1007/BFb0032072
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-52826-5
Online ISBN: 978-3-540-47159-2
eBook Packages: Springer Book Archive