Citation
Xiaojun Liu, Eleftherios Matsikoudis, Edward A. Lee. "Modeling Timed Concurrent Systems using Generalized Ultrametrics". Technical report, EECS Department, UC Berkeley, May, 2006.

Abstract
Timed concurrent systems are 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, which are sets of (semantically) time-stamped events. The denotational semantics of such systems is traditionally formulated in a metric space. In this metric space, causal components are modeled by 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.

Electronic downloads

• http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-45.html

• HTML

  Xiaojun Liu, Eleftherios Matsikoudis, Edward A. Lee. <a
  href="http://chess.eecs.berkeley.edu/pubs/120.html"
  ><i>Modeling Timed Concurrent Systems using
  Generalized Ultrametrics</i></a>, Technical
  report,  EECS Department, UC Berkeley, May, 2006.

• Plain text

  Xiaojun Liu, Eleftherios Matsikoudis, Edward A. Lee.
  "Modeling Timed Concurrent Systems using Generalized
  Ultrametrics". Technical report,  EECS Department, UC
  Berkeley, May, 2006.

• BibTeX

  @techreport{LiuMatsikoudisLee06_ModelingTimedConcurrentSystemsUsingGeneralizedUltrametrics,
      author = {Xiaojun Liu and Eleftherios Matsikoudis and Edward
                A. Lee},
      title = {Modeling Timed Concurrent Systems using
                Generalized Ultrametrics},
      institution = {EECS Department, UC Berkeley},
      month = {May},
      year = {2006},
      abstract = {Timed concurrent systems are 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, which are
                sets of (semantically) time-stamped events. The
                denotational semantics of such systems is
                traditionally formulated in a metric space. In
                this metric space, causal components are modeled
                by 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.},
      URL = {http://chess.eecs.berkeley.edu/pubs/120.html}
  }
  

Posted by Mary Stewart on 15 May 2006.
For additional information, see the Publications FAQ or contact webmaster at chess eecs berkeley edu.