Metric semantics for true concurrent real time

This paper investigates the use of a complete metric space framework for providing denotational semantics to a real-time process algebra. The study is carried out in a non-interleaving setting and is based on a timed extension of Langerak's bundle event structures, a variant of Winskel's event structures. The distance function is based on the amount of time to which event structures do ‘agree’. We show that this intuitive notion of distance is a pseudo metric (but not a metric) on the set of timed event structures. A generalisation to equivalence classes of timed event structures in which we abstract from event names and non-executable events (events that can never appear) is shown to be a complete ultra-metric space. We show that the resulting metric semantics is an abstraction of an existing cpo-based denotational and a related operational semantics for the considered language.

[1]  Christel Baier,et al.  Metric semantics from partial order semantics , 1997, Acta Informatica.

[2]  Ilaria Castellani,et al.  Flow Models of Distributed Computations: Three Equivalent Semantics for CCS , 1994, Inf. Comput..

[3]  David Murphy,et al.  Time and Duration in Nininterleaving Concurrency , 1993, Fundam. Informaticae.

[4]  Colin J. Fidge.  A constraint-oriented real-time process calculus , 1992, FORTE.

[5]  Glynn Winskel,et al.  Event Structure Semantics for CCS and Related Languages , 1982, ICALP.

[6]  Senro Saito,et al.  Using Timed CSP for Specification Verification and Simulation of Multimedia Synchronization , 1996, IEEE J. Sel. Areas Commun..

[7]  Jim Davies,et al.  Real-time LOTOS and Timed Observations , 1995, FORTE.

[8]  Rita Loogen,et al.  Modelling nondeterministic concurrent processes with event structures , 1991, Fundam. Informaticae.

[9]  Christel Baier,et al.  Denotational Semantics in the CPO and Metric Approach , 1994, Theor. Comput. Sci..

[10]  Mannes Poel,et al.  Layering of Real-Time Distributed Processes , 1994, FTRTFT.

[11]  Antoni W. Mazurkiewicz,et al.  Basic notions of trace theory , 1988, REX Workshop.

[12]  Christel Baier,et al.  How to Interpret and Establish Consistency Results for Semantics of Concurrent Programming Languages , 1997, Fundam. Informaticae.

[13]  Diego Latella,et al.  A Consistent Causality-Based View on a Timed Process Algebra Including Urgent Interactions , 1996, Formal Methods Syst. Des..

[14]  Joost-Pieter Katoen,et al.  Quantitative and Qualitative Extensions of Event Structures , 1996 .

[15]  Tommaso Bolognesi,et al.  Tableau methods to describe strong bisimilarity on LOTOS processes involving pure interleaving and enabling , 1994, FORTE.

[16]  Andrea Maggiolo-Schettini,et al.  Towards an Algebra for Timed Behaviours , 1992, Theor. Comput. Sci..

[17]  J. Bakker,et al.  Denotational models for programming lan-guages: Applications of banachs fixed point theorem , 1998 .

[18]  Rom Langerak,et al.  Bundle event structures: a non-interleaving semantics for LOTOS , 1992, FORTE.

[19]  Samson Abramsky,et al.  Domain theory , 1995, LICS 1995.

[20]  Joost-Pieter Katoen,et al.  Causal Ambiguity and Partial Orders in Event Structures , 1997, CONCUR.

[21]  Diego Latella,et al.  On Specifying Real-Time Systems in a Causality-Based Setting , 1996, FTRTFT.

[22]  Erik P. de Vink,et al.  Control flow semantics , 1996 .

[23]  Rajeev Alur,et al.  A Theory of Timed Automata , 1994, Theor. Comput. Sci..

[24]  Eric Goubault,et al.  Durations for Truly-Concurrent Transitions , 1996, ESOP.

[25]  J. W. de Bakker,et al.  Processes and the Denotational Semantics of Concurrency , 1982, Inf. Control..

[26]  Frits W. Vaandrager.  A simple definition for parallel composition of prime event structures , 1989 .

[27]  Christel Baier,et al.  Metric Semantics for True Concurrent Real Time , 1998, ICALP.

[28]  A. S. Klusener,et al.  Models and axioms for a fragment of real time process algebra , 1993 .

[29]  John Zic.  Time-constrained buffer specifications in CSP + T and timed CSP , 1994, TOPL.

[30]  Ilaria Castellani,et al.  Parallel Product of Event Structures , 1997, Theor. Comput. Sci..

[31]  Arend Rensink.  Posets for Configurations! , 1992, CONCUR.

[32]  Joseph Sifakis,et al.  An Overview and Synthesis on Timed Process Algebras , 1991, CAV.

[33]  Rom Langerak,et al.  Event Structures for Design and Transformation in LOTOS , 1991, FORTE.

[34]  Glynn Winskel,et al.  Petri Nets, Event Structures and Domains, Part I , 1981, Theor. Comput. Sci..

[35]  A. W. Roscoe,et al.  A Timed Model for Communicating Sequential Processes , 1986, Theor. Comput. Sci..