Completeness in real time process algebra
Recently, J.C.M. Baeten and J.A. Bergstra extended ACP with real time, resulting in a Real Time Process Algebra, called ACPρ [BB91]. They introduced an equational theory and an operational semantics. However, their work does not contain a completeness result nor does it contain the definitions to give proofs in detail. In this paper we introduce some machinery and a completeness result.
The operational semantics of [BB91] contains the notion of an idle step reflecting that a process can do nothing more then passing the time before performing a concrete action at a certain point in time. This idle step corresponds nicely to our intuition but it results in infinitary transition systems. In this paper we give a more abstract operational semantics, by abstracting from the idle step. Due to this simplification we can prove soundness and completeness easily. These results hold for the semantics of [BB91] as well, since both operational semantics induce the same equivalence relation between processes.
1985 Mathematics Subject Classification68Q10 68Q40 68Q45 68Q55
1982 CR CategoriesD.1.3 D.3.1 D.4.1 F.1.2 F.3.2
Key Words & PhrasesReal Time Process Algebra ACP Integration SOS
Unable to display preview. Download preview PDF.
- [BB90]J.C.M. Baeten and J.A. Bergstra. Process algebra with signals and conditions. Report P9008, University of Amsterdam, Amsterdam, 1990.Google Scholar
- [BB91]J.C.M. Baeten and J.A. Bergstra. Real time process algebra. Journal of Formal Aspects of Computing Science, 3(2):142–188, 1991.Google Scholar
- [BK84]J.A. Bergstra and J.W. Klop. Process algebra for synchronous communication. Information and Computation, 60(1/3):109–137, 1984.Google Scholar
- [BW90]J.C.M. Baeten and W.P. Weijland. Process algebra. Cambridge Tracts in Theoretical Computer Science 18. Cambridge University Press, 1990.Google Scholar
- [Gla87]R.J. van Glabbeek. Bounded nondeterminism and the approximation induction principle in process algebra. In F.J. Brandenburg, G. Vidal-Naquet, and M. Wirsing, editors, Proceedings STACS 87, volume 247 of Lecture Notes in Computer Science, pages 336–347. Springer-Verlag, 1987.Google Scholar
- [Gro89]J.F. Groote. Transition system specifications with negative premises. Report CS-R8950, CWI, Amsterdam, 1989. An extended abstract appeared in J.C.M. Baeten and J.W. Klop, editors, Proceedings CONCUR 90, Amsterdam, LNCS 458, pages 332–341. Springer-Verlag, 1990.Google Scholar
- [Gro90]J.F. Groote. Specification and verification of real time systems in ACP. Report CS-R9015, CWI, Amsterdam, 1990. An extended abstract appeared in L. Logrippo, R.L. Probert and H. Ural, editors, Proceedings 10 th International Symposium on Protocol Specification, Testing and Verification, Ottawa, pages 261–274, 1990.Google Scholar
- [Jef91]A. Jeffrey. Discrete timed CSP. Technical Report Memo 78, Chalmers University, Goteborg, 1991. This document also appeared in this volume.Google Scholar
- [Klu91]A.S. Klusener. Completeness in realtime process algebra. Report CS-R9106, CWI, Amsterdam, 1991.Google Scholar
- [Mil80]R. Milner. A Calculus of Communicating Systems, volume 92 of Lecture Notes in Computer Science. Springer-Verlag, 1980.Google Scholar
- [MT90]F. Moller and C. Tofts. A temporal calculus of communicating systems. In J.C.M. Baeten and J.W. Klop, editors, Proceedings CONCUR 90, Amsterdam, volume 458 of Lecture Notes in Computer Science, pages 401–415. Springer-Verlag, 1990.Google Scholar
- [NS90]X. Nicollin and J. Sifakis. ATP: An algebra for timed processes. Technical Report RT-C26, IMAG, Laboratoire de Génie informatique, Grenoble, 1990. An earlier version (RT-C16) appeared in M. Broy and C.B. Jones, editors, Proceedings IFIP Working Conference on Programming Concepts and Methods, Sea of Gallilea, Israel. North-Holland, 1990.Google Scholar
- [Par81]D.M.R. Park. Concurrency and automata on infinite sequences. In P. Deussen, editor, 5th GI Conference, volume 104 of Lecture Notes in Computer Science, pages 167–183. Springer-Verlag, 1981.Google Scholar
- [Plo81]G.D. Plotkin. A structural approach to operational semantics. Report DAIMI FN-19, Computer Science Department, Aarhus University, 1981.Google Scholar
- [RR88]M. Reed and A.W. Roscoe. A timed model for communicating sequential processes. Theoretical Computer Science, 58:249–261, 1988.Google Scholar
- [Wan90]Y. Wang. Real time behaviour of asynchronous agents. In J.C.M. Baeten and J.W. Klop, editors, Proceedings CONCUR 90, Amsterdam, volume 458 of Lecture Notes in Computer Science, pages 502–520. Springer-Verlag, 1990.Google Scholar