Abstract
The hierarchy of untimed equivalences is well understood for action-based systems. This is not the case for timed systems, where it is, for example, possible to detect concurrency by single timed action execution. To clarify the connection between equivalences in timed systems, a timed version of configuration structures is introduced together with timed equivalence notions adapted from untimed equivalences. There actions (events) have an occurrence time and a duration. The result of this paper is that all timed versions of the equivalences from [15] have the same relative discriminating power as in the untimed case, except that interleaving and step (for trace and bisimulation) equivalences coincide if systems are considered where every action must have a positive duration.
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References
Aceto, L., Murphy, D.: On the ill-timed but well-caused. In: Best [6], pp. 97–111
Aceto, L., Murphy, D.: Timing and causality in process algebra. Acta Informatica 33, 317–350 (1996)
Bednarczyk, M.A.: Hereditary history preserving bisimulation or what is the power of the future perfect in program logics. Technical report, Institute of Computer Science, Polish Academy of Science (1991)
Bergstra, J.A., Fokkink, W., Ponse, A.: Process algebra with recursive operations. In: Bergstra et al. [5], pp. 333–389
Bergstra, J.A., Ponse, A., Smolka, S.A. (eds.): Handbook of Process Algebra. North-Holland, Amsterdam (2001)
Best, E. (ed.): CONCUR 1993. LNCS, vol. 715. Springer, Heidelberg (1993)
Boudol, G., Castellani, I.: On the semantics of concurrency: Partial orders and transition systems. In: Ehrig, H., Levi, G., Montanari, U. (eds.) CAAP 1987 and TAPSOFT 1987. LNCS, vol. 249, pp. 123–137. Springer, Heidelberg (1987)
Chen, X.J., Corradini, F.: On the specification and verification of performance properties for a timed process algebra. In: Johnson, M. (ed.) AMAST 1997. LNCS, vol. 1349, pp. 123–137. Springer, Heidelberg (1997)
Corradini, F.: Absolute versus relative time in process algebras. Information and Computation 156, 122–172 (2000)
Degano, P., Nicola, R.D., Montanari, U.: Observational equivalences for concurrency models. In: Wirsing, M. (ed.) Formal Description of Programming Concepts – III, Proceedings of the 3th IFIP WG 2.2 working conference, Ebberup 1986, pp. 105–129. North-Holland, Amsterdam (1987)
Fecher, H.: A completed hierarchy of true concurrent equivalences. Information Processing Letters 89(5), 261–265 (2004)
R.: v. Glabbeek. The linear time–branching time spectrum II: The semantics of sequential systems with silent moves (extended abstract). In: Best [6], pp. 66–81
R.: v. Glabbeek. The linear time–branching time spectrum I. The semantics of concrete, sequential processes. In: Bergstra et al. [5], pp. 3–99
Glabbeek, R.v., Goltz, U.: Refinement of actions in causality based models. In: de Bakker, J.W., de Roever, W.-P., Rozenberg, G. (eds.) REX 1989. LNCS, vol. 430, pp. 267–300. Springer, Heidelberg (1990)
Glabbeek, R.v., Goltz, U.: Refinement of actions and equivalence notions for concurrent systems. Acta Informatica 37, 229–327 (2001)
Glabbeek, R.v., Plotkin, G.D.: Configuration structures. In: Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science, pp. 199–209. IEEE Computer Society Press, Los Alamitos (1995)
Glabbeek, R.v., Vaandrager, F.: Petri net models for algebraic theories of concurrency. In: de Bakker, J.W., Nijman, A.J., Treleaven, P.C. (eds.) PARLE 1987. LNCS, vol. 259, pp. 224–242. Springer, Heidelberg (1987)
Gorrieri, R., Rensink, A.: Action refinement. In: Bergstra et al. [5], pp. 1047– 1147
Gorrieri, R., Roccetti, M., Stancampiano, E.: A theory of processes with durational actions. Theoretical Computer Science 140, 73–94 (1995)
Hoare, C.A.R.: Communications Sequential Processes. International Series in Computer Science. Prentice-Hall, Englewood Cliffs (1985)
Katoen, J.-P., Langerak, R., Latella, D., Brinksma, E.: On specifying real-time systems in a causality-based setting. In: Jonsson, B., Parrow, J. (eds.) FTRTFT 1996. LNCS, vol. 1135, pp. 385–404. Springer, Heidelberg (1996)
Milner, R.: Calculi for synchrony and asynchrony. Theoretical Computer Science 25, 267–310 (1983)
Murphy, D.: Time and duration in noninterleaving concurrency. Fundamenta Informaticae 19, 403–416 (1993)
Pomello, L.: Some Equivalence Notions for Concurrent Systems. An Overview. In: Rozenberg, G. (ed.) APN 1985. LNCS, vol. 222, pp. 381–400. Springer, Heidelberg (1986)
Rabinovich, A., Trakhtenbrot, B.A.: Behavior structures and nets. Fundamenta Informaticae 11(4), 357–404 (1988)
Virbitskaite, I.B.: Observational semantics for timed event structures. In: Bjørner, D., Broy, M., Zamulin, A.V. (eds.) PSI 2001. LNCS, vol. 2244, pp. 214–224. Springer, Heidelberg (2001)
Wang, Y.: CCS+time = an interleaving model for real time systems. In: Leach Albert, J., Monien, B., Rodríguez-Artalejo, M. (eds.) ICALP 1991. LNCS, vol. 510, pp. 217–228. Springer, Heidelberg (1991)
Winskel, G.: An introduction to event structures. In: de Bakker, J.W., de Roever, W.-P., Rozenberg, G. (eds.) Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency. LNCS, vol. 354, pp. 364–397. Springer, Heidelberg (1989)
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Fecher, H. (2004). The Influence of Durational Actions on Time Equivalences. In: Lakhnech, Y., Yovine, S. (eds) Formal Techniques, Modelling and Analysis of Timed and Fault-Tolerant Systems. FTRTFT FORMATS 2004 2004. Lecture Notes in Computer Science, vol 3253. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30206-3_17
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DOI: https://doi.org/10.1007/978-3-540-30206-3_17
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