Modeling Timed Concurrent Systems

  • Xiaojun Liu
  • Eleftherios Matsikoudis
  • Edward A. Lee
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4137)


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.


Hybrid System Contracting Function Concurrent System Ultrametric Space Denotational Semantic 
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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Xiaojun Liu
    • 1
  • Eleftherios Matsikoudis
    • 2
  • Edward A. Lee
    • 2
  1. 1.Sun Microsystems, Inc. 
  2. 2.University of CaliforniaBerkeley

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