Abstract
We study the equational theory of Timed CCS as proposed by Wang Yi in CONCUR’90. Common to Wang Yi’s paper, we particularly focus on a class of linearly-ordered time domains exemplified by the positive real or rational numbers. We show that, even when the set of basic actions is a singleton, there are parallel Timed CCS processes that do not have any sequential equivalent and thus improve on the Gap Theorem for Timed CCS presented by Godskesen and Larsen in FSTTCS’92. Furthermore, we show that timed bisimilarity is not finitely based both for single-sorted and two-sorted presentations of Timed CCS. We further strengthen this result by showing that, unlike in some other process algebras, adding the untimed or the timed left-merge operator to the syntax and semantics of Timed CCS does not solve the axiomatizability problem.
The work of the authors has been partially supported by the project “The Equational Logic of Parallel Processes” (nr. 060013021) of The Icelandic Research Fund.
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
Aceto, L., Jeffrey, A.: A complete axiomatization of timed bisimulation for a class of timed regular behaviours. TCS 152(2), 251–268 (1995)
Alur, R., Dill, D.L.: Automata for modeling real-time systems. In: Paterson, M.S. (ed.) Automata, Languages and Programming. LNCS, vol. 443, pp. 322–335. Springer, Heidelberg (1990)
Bergstra, J.A., Klop, J.W.: Process algebra for synchronous communication. I&C 60(1-3), 109–137 (1984)
Baeten, J.C.M., Middelburg, C.A.: Process algebra with timing. Springer, Heidelberg (2002)
Godskesen, J.C., Larsen, K.G.: Real-time calculi and expansion theorems. In: Shyamasundar, R.K. (ed.) Foundations of Software Technology and Theoretical Computer Science. LNCS, vol. 652, pp. 302–315. Springer, Heidelberg (1992)
Jeffrey, A., Schneider, S., Vaandrager, F.W.: A comparison of additivity axioms in timed transition systems. Report CS-R9366, CWI, Amsterdam (1993)
Milner, R.: Communication and Concurrency. Prentice-Hall, Englewood Cliffs (1989)
Milner, R., Moller, F.: Unique decomposition of processes. TCS 107(2), 357–363 (1993)
Moller, F.: Axioms for Concurrency. Ph.D. Thesis, University of Edinburgh (1989)
Moller, F., Tofts, C.M.N.: A temporal calculus of communicating systems. In: Baeten, J.C.M., Klop, J.W. (eds.) CONCUR 1990. LNCS, vol. 458, pp. 401–415. Springer, Heidelberg (1990)
Moller, F.: The importance of the left merge operator in process algebras. In: Paterson, M.S. (ed.) Automata, Languages and Programming. LNCS, vol. 443, pp. 752–764. Springer, Heidelberg (1990)
Yi, W.: Real-time behaviour of asynchronous agents. In: Baeten, J.C.M., Klop, J.W. (eds.) CONCUR 1990. LNCS, vol. 458, pp. 502–520. Springer, Heidelberg (1990)
Yi, W.: CCS + time = an interleaving model for real time systems. In: Leach Albert, J., Monien, B., Rodríguez-Artalejo, M. (eds.) Automata, Languages and Programming. LNCS, vol. 510, pp. 217–228. Springer, Heidelberg (1991)
Yi, W.: A calculus of real time systems. PhD thesis, Chalmers University of Technology (1991)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Aceto, L., Ingólfsdóttir, A., Mousavi, M. (2007). Impossibility Results for the Equational Theory of Timed CCS. In: Mossakowski, T., Montanari, U., Haveraaen, M. (eds) Algebra and Coalgebra in Computer Science. CALCO 2007. Lecture Notes in Computer Science, vol 4624. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73859-6_6
Download citation
DOI: https://doi.org/10.1007/978-3-540-73859-6_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73857-2
Online ISBN: 978-3-540-73859-6
eBook Packages: Computer ScienceComputer Science (R0)