Encoding Asynchronous Interactions Using Open Petri Nets

We present an encoding for (bound) processes of the asynchronous CCS with replication into open Petri nets: ordinary Petri nets equipped with a distinguished set of open places. The standard token game of nets models the reduction semantics of the calculus; the exchange of tokens on open places models the interactions between processes and their environment. The encoding preserves strong and weak CCS asynchronous bisimilarities: it thus represents a relevant step in establishing a precise correspondence between asynchronous calculi and (open) Petri nets. The work is intended as fostering the technology transfer between these formalisms: as an example, we discuss how some results on expressiveness can be transferred from the calculus to nets and back.

[1]  Herman Geuvers,et al.  Constructive analysis, types and exact real numbers , 2007, Mathematical Structures in Computer Science.

[2]  Roberto Gorrieri,et al.  Distributed semantics for the pi-calculus based on Petri nets with inhibitor arcs , 2009, J. Log. Algebraic Methods Program..

[3]  Vladimiro Sassone,et al.  A Congruence for Petri Nets , 2005, PNGT@ICGT.

[4]  Frank D. Valencia,et al.  On the Expressive Power of Restriction and Priorities in CCS with Replication , 2009, FoSSaCS.

[5]  Robin Milner,et al.  Theories for the Global Ubiquitous Computer , 2004, FoSSaCS.

[6]  Vladimiro Sassone,et al.  High-Level Petri Nets as Type Theories in the Join Calculus , 2001, FoSSaCS.

[7]  Roberto Gorrieri,et al.  SCONE: A Simple Calculus of Nets , 1990, CONCUR.

[8]  Gian Luigi Ferrari,et al.  Event Based Service Coordination over Dynamic and Heterogeneous Networks , 2006, ICSOC.

[9]  Fabio Gadducci Graph rewriting for the pi-calculus , 2007, Math. Struct. Comput. Sci..

[10]  Wolfgang Reisig,et al.  Lectures on Concurrency and Petri Nets , 2003, Lecture Notes in Computer Science.

[11]  Bengt Jonsson,et al.  CONCUR ’94: Concurrency Theory , 1994, Lecture Notes in Computer Science.

[12]  Maciej Koutny,et al.  A compositional Petri net translation of general π-calculus terms , 2008, Formal Aspects of Computing.

[13]  Robin Milner,et al.  Bigraphs for Petri Nets , 2003, Lectures on Concurrency and Petri Nets.

[14]  Robin Milner,et al.  On Observing Nondeterminism and Concurrency , 1980, ICALP.

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

[16]  Robin Milner,et al.  Barbed Bisimulation , 1992, ICALP.

[17]  Petr Jancar Undecidability of Bisimilarity for Petri Nets and Some Related Problems , 1995, Theor. Comput. Sci..

[18]  Nadia Busi,et al.  A process algebraic view of shared dataspace coordination , 2008, J. Log. Algebraic Methods Program..

[19]  Ekkart Kindler,et al.  A Compositional Partial Order Semantics for Petri Net Components , 1997, ICATPN.

[20]  Gérard Boudol,et al.  Asynchrony and the Pi-calculus , 1992 .

[21]  Julian Rathke,et al.  Making the Unobservable, Unobservable , 2009, Electron. Notes Theor. Comput. Sci..

[22]  Maciej Koutny,et al.  A Petri Net Semantics of a Simple Process Algebra for Mobility , 2005, EXPRESS.

[23]  Gianfranco Balbo,et al.  Application and Theory of Petri Nets 1997 , 1997 .

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

[25]  Nadia Busi,et al.  Expired data collection in shared dataspaces , 2003, Theor. Comput. Sci..

[26]  Irène Guessarian,et al.  Semantics of systems of concurrent processes : LITP Spring School on Theoretical Computer Science, La Roche Posay, France, April 23-27, 1990, proceedings , 1990 .

[27]  Wil M.P. van der Aalst,et al.  Pi calculus versus petri nets: let us eat humble pie rather than further inflate the Pi hype , 2005 .

[28]  Pierre America,et al.  ECOOP'91 European Conference on Object-Oriented Programming , 1991, Lecture Notes in Computer Science.

[29]  Davide Sangiorgi,et al.  On Bisimulations for the Asynchronous pi-Calculus , 1996, Theor. Comput. Sci..

[30]  Mogens Nielsen,et al.  Decidability Issues for Petri Nets - a survey , 1994, Bull. EATCS.

[31]  Robin Milner,et al.  Pure bigraphs: Structure and dynamics , 2006, Inf. Comput..

[32]  Winfried Lamersdorf,et al.  Service-Oriented Computing - ICSOC 2006, 4th International Conference, Chicago, IL, USA, December 4-7, 2006, Proceedings , 2006, ICSOC.

[33]  A Di Pisa,et al.  Compositional Semantics for Open Petri Nets based on Deterministic Processes , 2001 .

[34]  Walter Vogler,et al.  Modular Construction and Partial Order Semantics of Petri Nets , 1992, Lecture Notes in Computer Science.

[35]  Davide Sangiorgi,et al.  On the bisimulation proof method , 1998, Mathematical Structures in Computer Science.

[36]  Ursula Goltz CCS and Petri Nets , 1990, Semantics of Systems of Concurrent Processes.

[37]  Mario Tokoro,et al.  An Object Calculus for Asynchronous Communication , 1991, ECOOP.

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

[39]  Maurizio Gabbrielli,et al.  Comparing Recursion, Replication, and Iteration in Process Calculi , 2004, ICALP.

[40]  Insup Lee,et al.  CONCUR '95: Concurrency Theory , 1995, Lecture Notes in Computer Science.

[41]  Rocco De Nicola,et al.  KLAIM: A Kernel Language for Agents Interaction and Mobility , 1998, IEEE Trans. Software Eng..

[42]  M. Nielsen,et al.  Decidability Issues for Petri Nets , 1994 .

[43]  Matthew Hennessy,et al.  Testing Theories for Asynchronous Languages , 1998, FSTTCS.

[44]  Rocco De Nicola,et al.  A Theory of "May" Testing for Asynchronous Languages , 1999, FoSSaCS.

[45]  Roland Meyer,et al.  A Practical Approach to Verification of Mobile Systems Using Net Unfoldings , 2008, Petri Nets.

[46]  Wolfgang Reisig Petri Nets: An Introduction , 1985, EATCS Monographs on Theoretical Computer Science.

[47]  Vladimiro Sassone,et al.  Characterizing Behavioural Congruences for Petri Nets , 1995, CONCUR.

[48]  Irène Guessarian Semantics of Systems of Concurrent Processes , 1990, Lecture Notes in Computer Science.

[49]  Roberto Gorrieri,et al.  A Petri Net Semantics for pi-Calculus , 1995, CONCUR.

[50]  Tilak Agerwala,et al.  Comments on capabilities, limitations and “correctness” of Petri nets , 1973, ISCA '73.

[51]  Rocco De Nicola,et al.  Asynchronous Observations of Processes , 1998, FoSSaCS.

[52]  Gérard Berry,et al.  The chemical abstract machine , 1989, POPL '90.