A Modular LTS for Open Reactive Systems

The theory of reactive systems (RSs) represents a fruitful proposal for deriving labelled transition systems (LTSs) from unlabelled ones. The synthesis of an LTS allows for the use of standard techniques in the analysis of systems, as witnessed by the widespread adoption of behavioral semantics. Recent proposals addressed one of the main drawbacks of RSs, namely, its restriction to the analysis of ground (i.e., completely specified) systems. A still unresolved issue concerns the lack of a presentation via inference rules for the derived LTS, thus hindering the modularity of the presentation. Our paper considers open RSs. We first introduce a variant of the current proposal based on "luxes": our technique is applicable to a larger number of case studies and, under some conditions, it synthesises a smaller LTS. Then, we illustrate how the LTS derived by using our approach can be equipped with a SOS-like presentation via an encoding into tile systems.

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

[2]  John Power An Abstract Formulation for Rewrite Systems , 1989, Category Theory and Computer Science.

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

[4]  Roberto Bruni,et al.  Symmetric monoidal and cartesian double categories as a semantic framework for tile logic , 2002, Mathematical Structures in Computer Science.

[5]  Paul H. Palmquist The double category of adjoint squares , 1971 .

[6]  Luca Cardelli,et al.  Mobile Ambients , 1998, FoSSaCS.

[7]  Alexander Kurz,et al.  Algebra and Coalgebra in Computer Science, Third International Conference, CALCO 2009, Udine, Italy, September 7-10, 2009. Proceedings , 2009, CALCO.

[8]  S. Maclane,et al.  Categorical Algebra , 2007 .

[9]  Vladimiro Sassone,et al.  Labels from Reductions: Towards a General Theory , 2005, CALCO.

[10]  Fabio Gadducci,et al.  Labelled Transitions for Mobile Ambients (As Synthesized via a Graphical Encoding) , 2008, EXPRESS.

[11]  R. Street,et al.  Review of the elements of 2-categories , 1974 .

[12]  Kousha Etessami,et al.  Optimizing Büchi Automata , 2000, CONCUR.

[13]  Vladimiro Sassone,et al.  Deriving Bisimulation Congruences using 2-categories , 2003, Nord. J. Comput..

[14]  Roberto Bruni,et al.  Deriving Weak Bisimulation Congruences from Reduction Systems , 2005, CONCUR.

[15]  Andrew M. Pitts,et al.  Category Theory and Computer Science , 1987, Lecture Notes in Computer Science.

[16]  Francesco Zappa Nardelli,et al.  Behavioural Theory for Mobile Ambients , 2004, IFIP TCS.

[17]  Marsha Chechik,et al.  CONCUR 2008 - Concurrency Theory, 19th International Conference, CONCUR 2008, Toronto, Canada, August 19-22, 2008. Proceedings , 2008, CONCUR.

[18]  Robin Milner,et al.  Deriving Bisimulation Congruences for Reactive Systems , 2000, CONCUR.

[19]  G. Plotkin,et al.  Proof, language, and interaction: essays in honour of Robin Milner , 2000 .

[20]  Fabio Gadducci,et al.  Reactive Systems, Barbed Semantics, and the Mobile Ambients , 2009, FoSSaCS.

[21]  Vincent Danos,et al.  Transactions in RCCS , 2005, CONCUR.

[22]  Ian Stark,et al.  Free-Algebra Models for the pi-Calculus , 2005, FoSSaCS.