A congruence relation for sPBC

Abstract In this paper we define a congruence relation for regular terms of sPBC (stochastic Petri Box Calculus), by means of which we identify those processes that have the same behaviour, not only in terms of the multiactions that they can perform, but also taking into account the stochastic information that they have associated. In order to define this equivalence relation we have to define an adequate semantics for the synchronization operator, as well as a new labelled transition system for regular terms of sPBC.

[1]  Raymond R. Devillers,et al.  The box calculus: a new causal algebra with multi-label communication , 1992, Advances in Petri Nets: The DEMON Project.

[2]  Jane Hillston,et al.  A compositional approach to performance modelling , 1996 .

[3]  J. Hillston.  The nature of synchronisation , 1994 .

[4]  Wolfgang Reisig,et al.  Lectures on Petri Nets II: Applications , 1996, Lecture Notes in Computer Science.

[5]  Mogens Nielsen,et al.  Application and Theory of Petri Nets 2000: 21st International Conference, ICATPN 2000 Aarhus, Denmark, June 26–30, 2000 Proceedings , 2000, ICATPN.

[6]  Roberto Gorrieri,et al.  A Tutorial on EMPA: A Theory of Concurrent Processes with Nondeterminism, Priorities, Probabilities and Time , 1998, Theor. Comput. Sci..

[7]  Maciej Koutny,et al.  Operational Semantics for the Petri Box Calculus , 1994, CONCUR.

[8]  David de Frutos-Escrig,et al.  Extending the Petri Box Calculus with Time , 2001, ICATPN.

[9]  Maciej Koutny,et al.  A Refined View of the Box Algebra , 1995, Application and Theory of Petri Nets.

[10]  Valentín Valero Ruiz,et al.  Introducing the Iteration in sPBC , 2004, FORTE.

[11]  Mario Bravetti,et al.  Compositional Asymmetric Cooperations for Process Algebras with Probabilities, Priorities, and Time , 2000, MTCS.

[12]  Marina Ribaudo,et al.  Stochastic Petri net semantics for stochastic process algebras , 1995, Proceedings 6th International Workshop on Petri Nets and Performance Models.

[13]  Maciej Koutny,et al.  Petri Net Algebra , 2001, Monographs in Theoretical Computer Science An EATCS Series.

[14]  Marco Ajmone Marsan,et al.  Modelling with Generalized Stochastic Petri Nets , 1995, PERV.

[15]  John G. Kemeny,et al.  Finite Markov chains , 1960 .

[16]  Robin Milner,et al.  Communication and concurrency , 1989, PHI Series in computer science.

[17]  Jos C. M. Baeten,et al.  The Total Order Assumption , 1992, NAPAW.

[18]  Giorgio De Michelis,et al.  Application and Theory of Petri Nets 1995 , 1995 .

[19]  Maciej Koutny,et al.  A Compositional Model of Time Petri Nets , 2000, ICATPN.

[20]  Kim G. Larsen,et al.  Bisimulation through Probabilistic Testing , 1991, Inf. Comput..

[21]  Maciej Koutny,et al.  A Unified Model for Nets and Process Algebras , 2001, Handbook of Process Algebra.

[22]  David de Frutos-Escrig,et al.  SPBC: a Markovian extension of finite Petri box calculus , 2001, Proceedings 9th International Workshop on Petri Nets and Performance Models.

[23]  John G. Kemeny,et al.  Finite Markov Chains. , 1960 .

[24]  Wolfgang Reisig,et al.  Application and Theory of Petri Nets , 1982, Informatik-Fachberichte.

[25]  Joost-Pieter Katoen,et al.  Process algebra for performance evaluation , 2002, Theor. Comput. Sci..

[26]  Valentín Valero Ruiz,et al.  A new synchronization in finite stochastic Petri box calculus , 2003, Third International Conference on Application of Concurrency to System Design, 2003. Proceedings..

[27]  H. Hermanns,et al.  Syntax , Semantics , Equivalences , and Axioms for MTIPP y , 1994 .

[28]  Maciej Koutny,et al.  Petri Nets, Process Algebras and Concurrent Programming Languages , 1996, Petri Nets.