A Connector Algebra for P/T Nets Interactions

A quite flourishing research thread in the recent literature on component-based system is concerned with the algebraic properties of various kinds of connectors for defining well-engineered systems. In a recent paper, an algebra of stateless connectors was presented that consists of five kinds of basic connectors, plus their duals. The connectors can be composed in series or in parallel and employing a simple 1-state buffer they can model the coordination language Reo. Pawel Sobocinski employed essentially the same stateful extension of connector algebra to provide semantics-preserving mutual encoding with some sort of elementary Petri nets with boundaries. In this paper we show how the tile model can be used to extend Sobocinski's approach to deal with P/T nets, thus paving the way towards more expressive connector models.

[1]  Roberto Bruni,et al.  Dynamic connectors for concurrency , 2002, Theor. Comput. Sci..

[2]  Gian Luigi Ferrari,et al.  Tile Formats for Located and Mobile Systems , 2000, Inf. Comput..

[3]  Pawel Sobocinski,et al.  Representations of Petri Net Interactions , 2010, CONCUR.

[4]  Joseph Sifakis,et al.  The Algebra of Connectors - Structuring Interaction in BIP , 2008, IEEE Trans. Computers.

[5]  Gordon D. Plotkin,et al.  A structural approach to operational semantics , 2004, J. Log. Algebraic Methods Program..

[6]  Ugo Montanari,et al.  An Algebraic Semantics for Structured Transition Systems and its Applications to Logic Programs , 1992, Theor. Comput. Sci..

[7]  Gheorghe Stefanescu,et al.  Reaction and Control I. Mixing Additive and Multiplicative Network Algebras , 1998, Log. J. IGPL.

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

[9]  Pawel Soboci 'nski.  A non-interleaving process calculus for multi-party synchronisation , 2009 .

[10]  Farhad Arbab,et al.  Tiles for Reo , 2009, WADT.

[11]  José Meseguer,et al.  Conditioned Rewriting Logic as a United Model of Concurrency , 1992, Theor. Comput. Sci..

[12]  Fabio Gadducci,et al.  The tile model , 2000, Proof, Language, and Interaction.

[13]  Roberto Bruni,et al.  A basic algebra of stateless connectors , 2006, Theor. Comput. Sci..

[14]  Alexander L. Wolf,et al.  Acm Sigsoft Software Engineering Notes Vol 17 No 4 Foundations for the Study of Software Architecture , 2022 .

[15]  Gordon D. Plotkin,et al.  The origins of structural operational semantics , 2004, J. Log. Algebraic Methods Program..

[16]  C. Petri.  Kommunikation mit Automaten , 1962 .

[17]  Paul Gastin,et al.  CONCUR 2010 - Concurrency Theory, 21th International Conference, CONCUR 2010, Paris, France, August 31-September 3, 2010. Proceedings , 2010, CONCUR.

[18]  José Luiz Fiadeiro,et al.  Categorical Semantics of Parallel Program Design , 1997, Sci. Comput. Program..

[19]  Joseph Sifakis,et al.  Causal semantics for the algebra of connectors , 2008, Formal Methods Syst. Des..

[20]  Martin Wirsing,et al.  Extraction of Structured Programs from Specification Proofs , 1999, WADT.

[21]  Luís Soares Barbosa,et al.  Specifying Software Connectors , 2004, ICTAC.

[22]  Zhiming Liu,et al.  Theoretical Aspects of Computing - ICTAC 2004, First International Colloquium, Guiyang, China, September 20-24, 2004, Revised Selected Papers , 2005, ICTAC.

[23]  Joseph Sifakis,et al.  Causal semantics for the algebra of connectors , 2010, Formal Methods Syst. Des..

[24]  Francesca Rossi,et al.  Graph Rewriting, Constraint Solving and Tiles for Coordinating Distributed Systems , 1999, Appl. Categorical Struct..

[25]  Roberto Bruni,et al.  Normal forms for algebras of connection , 2002, Theor. Comput. Sci..

[26]  Reiko Heckel,et al.  Compositional semantics for open Petri nets based on deterministic processes , 2005, Mathematical Structures in Computer Science.

[27]  Farhad Arbab,et al.  Reo: A Channel-based Coordination Model for Component Composition , 2005 .

[28]  Roberto Bruni,et al.  An interactive semantics of logic programming , 2001, Theory and Practice of Logic Programming.

[29]  Xinxin Liu,et al.  Compositionality through an Operational Semantics of Contexts , 1990, Journal of Logic and Computation.