Petri Nets and Bisimulation

Abstract Several categorical relationships (adjunctions) between models for concurrency have been established, allowing the translation of concepts and properties from one model to another. A central example is a coreflection between Petri nets and asynchronous transition systems. The purpose of the present paper is to illustrate the use of such relationships by transferring to Petri nets a general concept of bisimulation.

[1]  Glynn Winskel,et al.  Event Structures , 1986, Advances in Petri Nets.

[2]  Patrick Lincoln,et al.  Linear logic , 1992, SIGA.

[3]  K. Brown,et al.  Graduate Texts in Mathematics , 1982 .

[4]  M. Nivat.  Fiftieth volume of theoretical computer science , 1988 .

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

[6]  Luca Aceto,et al.  A Complete Axiomatization of Timed Bisimulation for a Class of Timed Regular Behaviours (Revised Version) , 1994 .

[7]  Marek Antoni Bednarczyk,et al.  Categories of asynchronous systems , 1987 .

[8]  Kim G. Larsen,et al.  A Constraint Oriented Proof Methodology Based on Modal Transition Systems , 1994, TACAS.

[9]  Kim G. Larsen,et al.  From Timed Automata to Logic - and Back , 1995, MFCS.

[10]  Kim G. Larsen,et al.  Automatic Synthesis of Real Time Systems , 1994, ICALP.

[11]  Ernst-Rüdiger Olderog,et al.  Nets, terms and formulas , 1991 .

[12]  Mogens Nielsen,et al.  Models for Concurrency , 1992 .

[13]  Glynn Winskel,et al.  Petri Nets, Algebras, Morphisms, and Compositionality , 1987, Inf. Comput..

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

[15]  Ilaria Castellani.  Bisimulations and Abstraction Homomorphisms , 1987, J. Comput. Syst. Sci..

[16]  David B. Benson,et al.  Bisimulation of Automata , 1988, Inf. Comput..

[17]  M. W. Shields.  Concurrent Machines , 1985, Comput. J..

[18]  Sten Agerholm,et al.  A HOL Basis for Reasoning about Functional Programs , 1994 .

[19]  Samson Abramsky,et al.  Handbook of logic in computer science. , 1992 .

[20]  Walter Vogler.  Deciding History Preserving Bisimilarity , 1991, ICALP.

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

[22]  Hans Hermes,et al.  Introduction to mathematical logic , 1973, Universitext.

[23]  Kim G. Larsen,et al.  Synthesizing Distinguishing Formulae for Real Time Systems , 1994, Nord. J. Comput..

[24]  Madhavan Mukund.  Petri Nets and Step Transition Systems , 1992, Int. J. Found. Comput. Sci..

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

[26]  R. Labrecque.  The Correspondence Theory , 1978 .

[27]  Ieke Moerdijk,et al.  A Completeness Theorem for Open Maps , 1994, Ann. Pure Appl. Log..

[28]  Madhavan Mukund,et al.  CCS, Locations and Asynchronous Transition Systems , 1992 .

[29]  Peter Bro Miltersen,et al.  Dynamic Algorithms for the Dyck Languages , 1995, WADS.

[30]  Mogens Nielsen,et al.  Bisimulations, Games, and Logic , 1994 .

[31]  Glynn Winskel,et al.  Bisimulation from Open Maps , 1994, Inf. Comput..

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

[33]  Grzegorz Rozenberg,et al.  Elementary Transition Systems , 1990, Theor. Comput. Sci..

[34]  A. Ingólfsdóttir.  A Semantic Theory for Value–Passing Processes Late Approach Part I: A Denotational Model and Its Complete Axiomatization , 1995 .