Modeling Timed Concurrent Systems
Timed concurrent systems are widely used in concurrent and distributed real-time software, modeling of hybrid systems, design of hardware systems (using hardware description languages), discrete-event simulation, and modeling of communication networks. They consist of concurrent components that communicate using timed signals, that is, sets of (semantically) time-stamped events. The denotational semantics of such systems is traditionally formulated in a metric space, wherein causal components are modeled as contracting functions. We show that this formulation excessively restricts the models of time that can be used. In particular, it cannot handle super-dense time, commonly used in hardware description languages and hybrid systems modeling, finite time lines, and time with no origin. Moreover, if we admit continuous-time and mixed signals (essential for hybrid systems modeling) or certain Zeno signals, then causality is no longer equivalent to its formalization in terms of contracting functions. In this paper, we offer an alternative semantic framework using a generalized ultrametric that overcomes these limitations.
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- 8.Gupta, V., Jagadeesan, R., Panangaden, P.: Approximate reasoning for real-time probabilistic processes. In: Proceedings of the First International Conference on the Quantitative Evaluation of Systems (QEST 2004), September 2004, pp. 304–313 (2004)Google Scholar
- 10.Kapur, A.: Interval and Point-Based Approaches to Hybrid Systems Verification. Ph.d., Stanford University, Uses super dense time (super-dense, superdense) (1997)Google Scholar
- 12.Lee, E.A., Sangiovanni-Vincentelli, A.: A framework for comparing models of computation. IEEE Transactions on CAD 17(12) (1998)Google Scholar
- 13.Lee, E.A., Varaiya, P.: Structure and Interpretation of Signals and Systems. Addison-Wesley, Reading (2003)Google Scholar
- 16.Liu, X.: Semantic foundation of the tagged signal model. Phd thesis, EECS Department, University of California (December 20, 2005)Google Scholar
- 17.Liu, X., Matsikoudis, E., Lee, E.A.: Modeling timed concurrent systems using generalized ultrametrics. Technical Report UCB/EECS-2006-45. EECS Department, University of California, Berkeley (May 1, 2006)Google Scholar
- 19.Manna, Z., Pnueli, A.: Verifying hybrid systems. Hybrid Systems, 4–35 (1992)Google Scholar
- 23.Reed, G.M., Roscoe, A.W.: Metric spaces as models for real-time concurrency. In: 3rd Workshop on Mathematical Foundations of Programming Language Semantics, London, UK, pp. 331–343 (1988)Google Scholar
- 24.van Breugel, F.: Comparative semantics for a real-time programming language with integration. In: Abramsky, S. (ed.) CAAP 1991 and TAPSOFT 1991. LNCS, vol. 493, pp. 397–411. Springer, Heidelberg (1991)Google Scholar
- 25.Yates, R.K.: Networks of real-time processes. In: Best, E. (ed.) CONCUR 1993. LNCS, vol. 715. Springer, Heidelberg (1993)Google Scholar