Abstract
We give an abstract axiomatic account of timed processes using monoids and their (partial and total) actions. Subsequently, we present categorical formulations thereof, including a novel characterisation of partial monoid actions as coalgebras for an evolution comonad. Adapting the approach of Turi and Plotkin [24], we then exhibit an abstract theory of well-behaved operational rules suitable for timed processes and, for discrete time, also derive a concrete syntactic format encompassing all rules we found in the literature.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This work is supported by EPSRC grant GR/M56333.
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
P. Aczel and P. F. Mendler. A final coalgebra theorem. In D. H. Pitt, D. E. Rydeheard, P. Dybjer, A. M. Pitts, and A. Poigné, editors, Category Theory and Computer Science, LNCS 389, pp. 357–365, 1989. Springer.
R. Alur and D. L. Dill A theory of timed automata. Theoretical Computer Science 25(2), pp. 183–235, 1994.
J.C.M. Baeten and J.W. Klop, editors. Concurrency Theory (CONCUR’ 90), LNCS 458, 1990. Springer.
J.C.M. Baeten and C.A. Middelburg. Process algebra with timing: real time and discrete time. In A. Ponse, and S. A. Smolka, editors. Handbook of Process Algebra. North-Holland, 2001 Bergstra et al. [5], chapter 10.
J. A. Bergstra, A. Ponse, and S. A. Smolka, editors. Handbook of Process Algebra. North-Holland, 2001.
J.A. Bergstra and J.W. Klop. Process algebra for synchronous communication. Information and Computation 60, pp. 109–137, 1984.
B. Bloom, S. Istrail, and A. R. Meyer. Bisimulation can’t be traced. Journal of the A CM 42(1), pp. 232–268, 1995.
R.J. van Glabbeek. The linear time-branching time spectrum I; the semantics of concrete, sequential processes. In A. Ponse, and S. A. Smolka, editors. Handbook of Process Algebra. North-Holland, 2001 Bergstra et al. [5], chapter 1, pages 3–99.
M. Hennessy and T. Regan. A process algebra for timed systems. Information and Computation 117, pp. 221–239, 1995.
C.A.R. Hoare. Communicating Sequential Processes. Prentice Hall, 1985.
J.J.M. Hooman and W.P. de Roever. Design and verification in real-time distributed computing: an introduction to compositional methods. In E. Brinksma, G. Scollo, and Chris A. Vissers, editors. International Conference on Protocol Specification, Testing and Verification, 1989. North-Holland.
A. Jeffrey. A linear time process algebra. InA. Skou, editors. Computer Aided Verification (CAV’ 91), LNCS 575, 1991. Springer Larsen and Skou [14], pp. 432–442.
A. S. A. Jeffrey, S. A. Schneider, and F. W. Vaandrager. A comparison of additivity axioms in timed transition systems. Technical Report CS-R9366, CWI, 1993.
K.G. Larsen and A. Skou, editors. Computer Aided Verification (CAV’ 91), LNCS 575, 1991. Springer.
W. Lawvere. Metric spaces, generalized logic, and closed categories. In Rendiconti del Seminario Matematico e Fisico di Milano, XLIII. Tipografia Fusi, 1973.
R. Milner. Communication and Concurrency. Prentice Hall, 1989.
F. Moller and C. Tofts. A temporal calculus of communicating systems. In J.W. Klop, editors. Concurrency Theory (CONCUR’ 90), LNCS 458, 1990. Springer Baeten and Klop [3], pp. 401–415.
X. Nicollin and J. Sifakis. An overview and synthesis on timed process algebras. In A. Skou, editors. Computer Aided Verification (CAV’ 91), LNCS 575, 1991. Springer Larsen and Skou [14], pp. 376–398.
X. Nicollin and J. Sifakis. The algebra of timed processes, ATP: Theory and application. Information and Computation 114, pp. 131–178, 1994.
G. D. Plotkin. A structural approach to operational semantics. Technical Report DAIMI FN-19, Computer Science Department, Aarhus University, 1981.
J. Power and H. Watanabe. Distributivity for a monad and a comonad. In B. Jacobs and J. Rutten, editors, Second Workshop on Coalgebraic Methods in Computer Science (CMCS’1999), volume 19 of ENTCS, 1999.
S. A. Schneider. An operational semantics for timed CSP. Technical Report PRG-TR-1-91, Oxford University, 1991.
D. Turi. Functorial Operational Semantics and its Denotational Dual. PhD thesis, Free University, Amsterdam, 1996.
D. Turi and G. Plotkin. Towards a mathematical operational semantics. In Twelfth Annual Symposium on Logic in Computer Science (LICS’ 97), pp. 280–291, 1997. IEEE Computer Society Press.
Y. Wang. Real-time behaviour of asynchronous agents. In J.W. Klop, editors. Concurrency Theory (CONCUR’ 90), LNCS 458, 1990. Springer Baeten and Klop [3], pp. 502–520.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kick, M. (2002). Bialgebraic Modelling of Timed Processes. In: Widmayer, P., Eidenbenz, S., Triguero, F., Morales, R., Conejo, R., Hennessy, M. (eds) Automata, Languages and Programming. ICALP 2002. Lecture Notes in Computer Science, vol 2380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45465-9_45
Download citation
DOI: https://doi.org/10.1007/3-540-45465-9_45
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43864-9
Online ISBN: 978-3-540-45465-6
eBook Packages: Springer Book Archive