Abstract
In this paper we study a special operator for sequential composition, which is defined relative to a dependency relation over the actions of a given system. The idea is that actions which are not dependent (intuitively because they share no common resources) do not have to wait for one another to proceed, even if they are composed sequentially. Such a notion has been studied before in a linear-time setting, but until recently there has been no systematic investigation in the context of process algebras.
We give a structural operational semantics for a process algebraic language containing such a sequential composition operator, which shows some interesting interplay with choice. We give a complete axiomatisation of strong bisimilarity and we show consistency of the operational semantics with an event-based denotational semantics developed recently by the second author. The axiom system allows to derive the communication closed layers law, which in the linear time setting has been shown to be a very useful instrument in correctness preserving transformations. We conclude with a couple of examples.
Research partially supported by the HCM Cooperation Network “EXPRESS» (Expressiveness of Languages for Concurrency), the Esprit Basic Research Working Group 6067 (CALIBAN) and a Graduiertenfürderungsstipendium of the University of Hildesheim
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
L. Aceto, B. Bloom, and F. Vaandrager. Turning SOS rules into equations. In Seventh Annual IEEE Symposium on Logic in Computer Science pages 113–124. IEEE, Computer Society Press, 1992. Full version available as CWI Report CS-R9218, June 1992, Amsterdam. To appear in the LICS 92 Special Issue of Information and Computation.
L. Aceto and M. Hennessy. Towards action-refinement in process algebras. Information and Computation, 103: 204–269, 1993.
J. C. M. Baeten and F. W. Vaandrager. An algebra for process creation. In J. W. de Bakker, 25 Jaar Semantiek - Liber Amicorum. Stichting Mathematisch Centrum, Amsterdam, Apr. 1989. Also availabe as: Report CS-R8907, CWI, Amsterdam.
J. C. M. Baeten and W. P. Weijland. Process Algebra. Cambridge University Press, 1990.
M. A. Bednarczyk. Categories of Asynchronous Systems. PhD thesis, University of Sussex, Oct. 1987. Available as Report 1/88, School of Cognitive and Computing Sciences, University of Sussex.
J. A. Bergstra and J. W. Klop. Algebra of communicating processes with abstraction. Theoretical Comput. Sci., 37 (1): 77–121, 1985.
B. Bloom, S. Istrail, and A. R. Meyer. Bisimulation can’t be traced. In Fifteenth Annual Symposium on the Principles of Programming Languages pages 229–239. ACM, 1988. Preliminary Report.
J. W. de Bakker, W.-P. de Roever, and G. Rozenberg, editors. Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, volume 354 of Lecture Notes in Computer Science. Springer-Verlag, 1989.
P. Degano and R. Gorrieri. An operational definition of action refinement. Technical Report TR-28/92, Università di Pisa, 1992. To appear in Information and Computation.
M. Fokkinga, M. Poel, and J. Zwiers. Modular completeness for communication closed layers. In E. Best, editor, Concur ‘83, volume 715 of Lecture Notes in Computer Science, pages 50–65. Springer-Verlag, 1992.
U. Goltz and N. Götz. Modelling a simple communication protocol in a language with action refinement. Draft version, 1991.
C. A. R. Hoare. Communicating Sequential Processes. Prentice-Hall, 1985.
W. Janssen, M. Poel, and J. Zwiers. Actions systems and action refinement in the development of parallel systems. In J. C. M. Baeten and J. F. Groote, editors, Concur ‘81, volume 527 of Lecture Notes in Computer Science, pages 298–316. Springer-Verlag, 1991.
A. Mazurkiewicz. Basic notions of trace theory. In de Bakker et al. [8], pages 285–363.
R. Milner. Communication and Concurrency. Prentice-Hall, 1989.
A. Rensink. Models and Methods for Action Refinement. PhD thesis, University of Twente, Enschede, Netherlands, Aug. 1993.
M. W. Shields. Concurrent machines. The Computer Journal, 28 (5): 449–465, 1985.
E. W. Stark. Concurrent transition systems. Theoretical Comput. Sci., 64: 221–269, 1989.
F. W. Vaandrager. Expressiveness results for process algebras. Report CS-R9301, Centre for Mathematics and Computer Science, 1993. Available by ftp: ftp.cwi.nl, pub/CWlreports/AP.
H. Wehrheim. Parametric action refinement. Hildesheimer Informatik-Berichte 18/93, Institut für Informatik, Universität Hildesheim, Nov. 1993. To be presented at PRO-COMET ‘84, San Miniato, June 1994.
J. Zwiers. Layering and action refinement for timed systems. In J. W. de Bakker, C. Huizing, W.-P. de Roever, and G. Rozenberg, editors, Real-Time: Theory in Practice, volume 600 of Lecture Notes in Computer Science. Springer-Verlag, 1991.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Rensink, A., Wehrheim, H. (1994). Weak Sequential Composition in Process Algebras. In: Jonsson, B., Parrow, J. (eds) CONCUR ’94: Concurrency Theory. CONCUR 1994. Lecture Notes in Computer Science, vol 836. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-48654-1_20
Download citation
DOI: https://doi.org/10.1007/978-3-540-48654-1_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58329-5
Online ISBN: 978-3-540-48654-1
eBook Packages: Springer Book Archive