On the ill-timed but well-caused
There has been considerable controversy in concurrency theory between the ‘interleaving’ and ‘true concurrency’ schools. The former school advocates associating a transition system with a process which captures concurrent execution via the interleaving of occurrences: the latter adopts more complex semantic structures to avoid reducing concurrency to interleaving.
In this paper we show that the two approaches are not irreconcilable. We define a timed process algebra where occurrences are associated with intervals of time, and give it a transition system semantics. This semantics has many of the advantages of the interleaving approach; the algebra admits an expansion theorem, and bisimulation semantics can be used as usual. Our transition systems, however, incorporate timing information, and this enables us to express concurrency: merely adding timing appropriately generalises transition systems to asynchronous transition systems, showing that time gives a link between true concurrency and interleaving. Moreover, we can provide a complete axiomatisation of bisimulation for our algebra; a result that is often problematic in a timed setting.
Another advantage of incorporating timing information into the calculus is that it allows a particularly simple definition of action refinement; this we present.
KeywordsTransition System Operational Semantic Label Transition System Process Algebra Local Clock
Unable to display preview. Download preview PDF.
- 1.L. Aceto, Relating distributed, temporal and causal observations of simple processes, Fundamenta Informaticae, Volume 17 (1992), Number 4, Pp. 369–397.Google Scholar
- 2.L. Aceto, D. Murphy, Timing and Causality in Process Algebra. In preparation.Google Scholar
- 3.L. Aceto and M. Hennessy, Towards action-refinement in process algebra, Information and Computation, Volume 103, Number 2 (1993).Google Scholar
- 4.T. Axford, Concurrent Programming: Fundamental Techniques for Real-Time and Parallel Software Design, Wiley, 1989Google Scholar
- 6.J. Baeten and W. Weijland, Process algebra, Cambridge Tracts in Theoretical Computer Science, Volume 18, Cambridge University Press, 1990.Google Scholar
- 7.M. Bednarczyk, Categories of asynchronous systems, Ph.D. thesis, Department of Computer Science, University of Sussex, 1987, available as Technical Report Number 3/87.Google Scholar
- 8.G. Boudol, I. Castellani, M. Hennessy, and A. Kiehn, A theory of processes with locality, Technical Report 13/91, Department of Computer Science, University of Sussex, 1991.Google Scholar
- 9.P. Darondeau and P. Degano. Caused trees, in Automata, Languages and Programming (B. Rovan, Ed.), Volume 372, Springer-Verlag LNCS, 1989.Google Scholar
- 10.J. Davies and S. Schneider, An introduction to timed CSP, Technical Report Number 75, Oxford University Computer Laboratory, 1989.Google Scholar
- 11.G. Ferrari, R. Gorrieri, and U. Montanari, Parametric Jaws for concurrency, manuscript, Dipartimento di Informatica, Universitá di Pisa, 1992.Google Scholar
- 12.R. van Glabbeek, Comparative concurrency semantics and refinement of actions, Ph.D. thesis, Vrije Universiteit te Amsterdam, 1990.Google Scholar
- 13.J. Godskesen and K. Larsen, Real-time calculi and expansion theorems, in Proceedings of the 1st North American Process Algebra Workshop, 1992.Google Scholar
- 14.R. Gorrieri, Refinement, atomicity and transactions for process description languages, Ph.D. thesis, Dipartimento di Informatica, Università di Pisa, 1991, available as Technical Report TD 2/91.Google Scholar
- 15.R. Gorrieri and M. Roccetti, Towards performance evaluation in process algebra. To appear in the proceedings of AMAST 1993.Google Scholar
- 16.M. Hennessy, Axiomatising Finite Concurrent Processes, SIAM Journal of Computing, Volume 17, Number 5, 1988.Google Scholar
- 17.M. Hennessy and T. Regan, A temporal process algebra, Technical Report 2/90, Department of Computer Science, University of Sussex, 1990.Google Scholar
- 18.C. Hoare, Communicating sequential processes, International series on computer science, Prentice-Hall, 1985.Google Scholar
- 19.M. Joseph and A. Goswami, Relating computation and time, Technical Report RR 138, Department of Computer Science, University of Warwick, 1985.Google Scholar
- 21.A. Mazurkiewicz, Traces, histories, graphs: Instances of a process monoid, in Mathematical Foundations of Computer Science, Volume 176, Springer-Verlag LNCS, 1984.Google Scholar
- 22.R. Milner, Communication and concurrency, International series on computer science, Prentice Hall International, 1989.Google Scholar
- 23.F. Moller and C. Tofts, A temporal calculus of communicating systems, in the Proceedings of Concur, Volume 459, Springer-Verlag LNCS, pp. 401–415, 1990.Google Scholar
- 24.D. Murphy, Intervals and actions in a timed process algebra, Technical Report Arbeitspapiere der GMD 680, Gesellschaft für Mathematik und Dataverarbeitung, St. Augustin, 1992, presented at MFPS '92 and submitted to Theoretical Computer Science.Google Scholar
- 25.X. Nicollin and J. Sifakis, The algebra of timed processes ATP: Theory and application, Technical Report RT-C26, Laboratoire de Génie Informatique de Grenoble, 1990.Google Scholar
- 26.G. Plotkin, A structurai approach to operational semantics, Technical Report DAIMI-FN-19, Computer Science Department, Århus University, 1981.Google Scholar
- 27.S. Schneider, An operational semantics for timed CSP, manuscript, Programming Research Group, Oxford University. To appear in Information and Computation.Google Scholar
- 28.V. Sassone, M. Nielsen and G. Winskel, A classification of models for concurrency, this volume.Google Scholar