Testing, betting and timed true concurrency
The testing methodology is both appealingly simple and powerful as a way of analysing the behaviour of processes. In this paper we extend it in three ways.
Firstly we show how to incorporate the testing methodology into models where the notion of observation is central, rather than that of participation; we do this by introducing the notion of betting. This gives us a testing paradigm for true concurrency models such as event structures.
Secondly we introduce various timed bets to extend the methodology to timed models. An intuitively attractive semantics that admits a clear notion of rapidity of response is obtained.
Thirdly we show how bets can be extended to causal bets that allow us to reason about the causal behaviour of systems. The assumption that causality is observable is a strong one, but it may be justified if we read ‘concurrent’ as ‘physically distributed’.
Finally we classify the various betting semantics, presenting a hierarchy of semantics of increasing power. The semantics are presented with respect to a timed event structure model; they could, however, be applied to any (timed) causal model.
KeywordsEvent Structure Testing Methodology Complete History Silent Event Communicate Sequential Process
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- 1.S. Abramsky, Observational Equivalence is Testing Equivalence, Theoretical Computer Science, Volume 53 (1987), Pp. 225–241.Google Scholar
- 2.L. Aceto, R. de Nicola, and A. Fantechi, Testing Equivalence for Event Structures, in Mathematical Models for the Semantics of Parallelism (M. Venturini-Zilli, Ed.), (1987), Springer-Verlag LNCS 280.Google Scholar
- 3.L. Aceto and M. Hennessy, Towards action-refinement in Process Algebra, Technical Report 3/88, Department of Computer Science, University of Sussex, 1988.Google Scholar
- 4.B. Bloom and A. Meyer, Experimenting with Process Equivalence, in Semantics for Concurrency, (1990), Springer-Verlag Workshops in Computing.Google Scholar
- 5.J. Davies and S. Schneider, An introduction to timed CSP, Technical Report Number 75, Oxford University Computing Laboratory, 1989.Google Scholar
- 6.P. Degano and U. Montanari, Concurrent Histories: A basis for observing distributed systems, Journal of Computer Systems Sciences, Volume 34 (1987), Pp. 442–461.Google Scholar
- 7.R. Gerth and A. Boucher, A timed failures model for communicating processes, in Automata, Languages and Programming, (1987), Springer-Verlag LNCS 267, (14th Coll.).Google Scholar
- 8.J. Gischer, The equational theory of pomsets, Theoretical Computer Science, Volume 61 (1989), Pp. 199–224.Google Scholar
- 9.M. Hennessy, Synchronous and asynchronous experiments on processes, Information and Control, Volume 51 (1983), Number 1, Pp. 58–75.Google Scholar
- 10.M. Hennessy and T. Regan, A Temporal Process Algebra, Technical Report 2/90, Department of Computer Science, University of Sussex, 1990.Google Scholar
- 11.C. Hoare, Communicating Sequential Processes, International series on computer science, Prentice-Hall, 1985.Google Scholar
- 12.M. Joseph and A. Goswami, Relating Computation and Time, Technical Report RR 138, Department of Computer Science, University of Warwick, 1985.Google Scholar
- 13.L. Lamport, On interprocess communication. Part I: Basic formalism, Distributed Computing, Volume 1 (1986), Pp. 77–85.Google Scholar
- 14.D. Murphy, Time, causality, and concurrency, Ph.D. thesis, Department of Mathematics, University of Surrey, 1989, Available as Technical Report CSC 90/R32, Department of Computing Science, University of Glasgow.Google Scholar
- 15.—, A Functorial Semantics of Timed Concurrency, In preparation, 1991.Google Scholar
- 16.—, Three papers on classical concurrency theory, Technical Report CSC 91/R5, Department of Computing Science, University of Glasgow, 1991.Google Scholar
- 17.W. Reisig, A Strong Part of Concurrency, in Advances in Petri Nets (G. Rozenberg, Ed.), (1987), Springer-Verlag LNCS 266.Google Scholar
- 18.M. Roncken and R. Gerth, A Denotational Semantics for Synchronous and Asynchronous Behaviour with Multiform Time, in Semantics for Concurrency (M. Kwiatkowska, M. Shields, and R. Thomas, Eds.), (1990), Springer-Verlag Workshops in Computing, Leicester, 1990.Google Scholar
- 19.A. Schettini and J. Winkowsi, Towards an algebra for timed behaviours, Technical report, Institute of Computer Science, Polish Academy of Sciences, 1990, To appear in Theoretical Computer Science.Google Scholar
- 20.G. Winskel, An introduction to Event Structures, in Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency (J. de Bakker, W. de Roever, and G. Rozenberg, Eds.), (1989), Springer-Verlag LNCS 354, Proceedings of REX 1988.Google Scholar