Relating processes with respect to speed
In this paper, we consider the problem of defining a preorder on concurrent processes which will distinguish between functionally behaviourally equivalent processes which operate at different speeds. As our basic framework, we use a subset of the calculus TCCS of [Mol90], a language for describing concurrent processes involving timing constraints.
There is an anomaly in timed process calculi such as TCCS which nullifies the possibility of defining such a preorder which is a precongruence. This anomaly arises due to the nature of the constructs in the calculus which force events to be executed without delay. To rectify this conflict, we define and motivate the above mentioned subcalculus, which we call ℓTCCS (loose TCCS), and define our relation over this language. ℓTCCS is precisely TCCS where all events may delay indefinitely before executing. We demonstrate why this is necessary in order for any sensible faster than relation to be a precongruence.
Upon providing the semantic definition of our “faster than” relation, we give results on the precongruicity of the relation and present a set of inequational laws.
KeywordsParallel Operator Operational Rule Process Algebra Process Term Communicate Sequential Process
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- [Aru90]Arun-Kumar, S., M. Hennessy, An Efficiency Preorder for Processes, University of Sussex Research Report No. 5/90, 1990.Google Scholar
- [Bae89]Baeten, J.C.M., J.A. Bergstra, Real Time Process Algebra, Preliminary Draft, 10/20/89, 1989.Google Scholar
- [CWB90]The Edinburgh Concurrency Workbench — Operating Instructions, University of Edinburgh Technical Report, 1990.Google Scholar
- [Gro90]Groote, J.F., Specification and Verification of Real Time Systems in ACP, Research Report No CS-R9015, Centre for Mathematics and Computer Science, Amsterdam, 1990.Google Scholar
- [Hen90]Hennessy, M., T. Regan, A Temporal Process Algebra Technical Report No. 2/90, University of Sussex Computer Science Department, April, 1990.Google Scholar
- [Mil80]Milner, R., A Calculus of Communicating Systems, Lecture Notes in Computer Science 92, Springer-Verlag, 1980.Google Scholar
- [Mil83]Milner, R., Calculi for Synchrony and Asynchrony, Theoretical Computer Science, Vol 25, 1983.Google Scholar
- [Mil89]Milner, R., Communication and Concurrency, Prentice-Hall International, 1989.Google Scholar
- [Mol90]Moller, F., C. Tofts, A Temporal Calculus of Communicating Systems, Proceedings of CONCUR'90 (Theories of Concurrency: Unification and Extension), Amsterdam, August 1990.Google Scholar
- [Nic90]Nicollin, X., J.L. Richier, J. Sifakis, J. Voiron, ATP: An Algebra for Timed Processes, Proceedings of IFIP Working Conference on Programming Concepts and Methods, North Holland, 1990.Google Scholar
- [Par81]Park, D.M.R., Concurrency and Automata on Infinite Sequences, Lecture Notes in Computer Science 104, Springer-Verlag, 1981.Google Scholar
- [Plo81]Plotkin, G.D., A Structured Approach to Operational Semantics, DAIMI FN-19, Computer Science Department, Aarhus University, 1981.Google Scholar
- [Ree86]Reed, G.M., A. Roscoe, A Timed Model for Communicating Sequential Processes, Proceedings of ICALP'86, Lecture Notes in Computer Science No 226, Springer Verlag, 1986.Google Scholar
- [Tof90]Tofts, C., Proof Systems and Pragmatics for Parallel Programming, PhD Thesis, University of Edinburgh, 1990.Google Scholar
- [Wan90]Wang Yi, Real-time Behaviour of Asynchronous Agents, Proceedings of CONCUR'90 (Theories of Concurrency: Unification and Extension), Amsterdam, August 1990.Google Scholar