Concurrent bisimulations in Petri nets

SummaryAfter various attempts, an equivalence relation is defined for labelled Petri nets, on the base of the concurrency semantics of net theory. This relation, called Fully Concurrent bisimulation and abbreviated FC-bisimulation, preserves the level of concurrency of visible operations and, under some conditions, allows to enforce injective labelling on them. Refinements of a visible operation are also defined and we show that, under some conditions, they preserve FC-bisimulation.

[1]  Ursula Goltz.  On Representing CCS Programs by Finite Petri Nets , 1988, MFCS.

[2]  Ursula Goltz,et al.  Equivalences and Refinement , 1990, Semantics of Systems of Concurrent Processes.

[3]  David Park,et al.  Concurrency and Automata on Infinite Sequences , 1981, Theoretical Computer Science.

[4]  Grzegorz Rozenberg,et al.  Subset Languages of Petri Nets , 1982, European Workshop on Applications and Theory of Petri Nets.

[5]  Carla Simone,et al.  A state transformation preorder over a class of EN systems , 1991, Applications and Theory of Petri Nets.

[6]  H. Pomello,et al.  Observing net behaviour , 1987 .

[7]  Grzegorz Rozenberg,et al.  Advances in Petri Nets 1988 , 1987, Lecture Notes in Computer Science.

[8]  P. S. Thiagarajan,et al.  Degrees of Non-Determinism and Concurrency: A Petri Net View , 1984, FSTTCS.

[9]  Roberto Gorrieri,et al.  An Exercise in Concurrency: a CSP Process as a Condition/ event System , 1988, European Workshop on Applications and Theory of Petri Nets.

[10]  Walter Vogler.  Bisimulation and Action Refinement , 1993, Theor. Comput. Sci..

[11]  Karl Martin Schmidt-Reindl,et al.  Notations and terminology on Petri Net theory , 1987 .

[12]  李幼升,et al.  Ph , 1989 .

[13]  Philippe Darondeau,et al.  Event Structures, Causal Trees, and Refinements , 1990, MFCS.

[14]  Roy H. Campbell,et al.  Formal semantics of a class of high-level primitives for coordinating concurrent processes , 2004, Acta Informatica.

[15]  Wolfgang Reisig,et al.  CSP-programs with individual tokens , 1984, European Workshop on Applications and Theory in Petri Nets.

[16]  Robin Milner,et al.  A Calculus of Communicating Systems , 1980, Lecture Notes in Computer Science.

[17]  Eike Best.  COSY: Its Relation to Nets and CSP , 1986, Advances in Petri Nets.

[18]  Giorgio De Michelis,et al.  Concurrency versus interleaving: an instructuve example , 1987, Bull. EATCS.

[19]  Raymond R. Devillers.  Maximality Preserving Bisimulation , 1992, Theor. Comput. Sci..

[20]  Carla Simone,et al.  A survey of equivalence notions for net based systems , 1992, Advances in Petri Nets: The DEMON Project.

[21]  Ursula Goltz,et al.  Equivalence Notions for Concurrent Systems and Refinement of Actions (Extended Abstract) , 1989, MFCS.

[22]  Luca Aceto,et al.  Towards Action-Refinement in Process Algebras , 1993, Inf. Comput..

[23]  J.J.C. Meijer,et al.  Refinement in branching time semantics , 1989 .

[24]  Walter Vogler.  Failures semantics based on interval semiwords is a congruence for refinement , 2005, Distributed Computing.

[25]  Rocco De Nicola,et al.  Observational equivalences for concurrency models , 1987, Formal Description of Programming Concepts.

[26]  Raymond R. Devillers,et al.  On the Definition of a Bisimulation Notion Based on Partial Words , 1988 .

[27]  Rob J. van Glabbeek,et al.  Petri Net Models for Algebraic Theories of Concurrency , 1987, PARLE.

[28]  Wilfried Brauer,et al.  A survey of behaviour and equivalence preserving refinements of Petri nets , 1991, Applications and Theory of Petri Nets.

[29]  Grzegorz Rozenberg,et al.  Advances in Petri Nets 1985 , 1985, Lecture Notes in Computer Science.

[30]  R. J. vanGlabbeek.  The refinement theorem for ST-bisimulation semantics , 1990 .

[31]  Raymond R. Devillers,et al.  Sequential and Concurrent Behaviour in Petri Net Theory , 1987, Theor. Comput. Sci..

[32]  Lucia Pomello,et al.  Some equivalence notions for concurrent systems. An overview , 1985, Applications and Theory in Petri Nets.

[33]  Ilaria Castellani,et al.  On the Semantics of Concurrency: Partial Orders and Transition Systems , 1987, TAPSOFT, Vol.1.

[34]  Ursula Goltz,et al.  Refinement of Actions in Causality Based Models , 1990, REX Workshop.

[35]  Giorgio De Michelis,et al.  Milner's Communicating Systems and Petri Nets , 1982, European Workshop on Applications and Theory of Petri Nets.