From action systems to modular systems

Jbcs, 1995

Inspired by Meseguer and Montanari's "Petri Nets are Monoids", we propose that a reification of a Petri net is a special kind of net morphism were the target object is enriched with all conceivable sequential and concurrent computations. Then it is proven that while reification of nets satisfies the vertical compositionality requirement (i.e., reifications compose), it lacks the horizontal compositionality requirement (i.e., reification does not distribute over parallel composition). To achieve both requirements, a new categorial semantic domain based on labeled transition systems with full concurrency, called nonsequential automata, is constructed. Again, a class of morphisms stands for reification and, in this framework, the diagonal compositionality requirement (i.e., both vertical and horizontal) is achieved. Adjunctions between both models are provided extending the approach of Winskel and Nielsen. The steps of abstraction involved in moving between models show that nonsequential automata are more concrete than Petri nets. Moreover, categories of Petri Nets are isomorphic to subcategories of nonsequential automata.

Proceedings First Asia-Pacific Conference on Quality Software, 2000

The formal verification of properties in reactive Real-Time system is crucial, as these systems are often safetycritical ones. Refinements is a relevant operation in synchronous languages. In this paper we argue that, in the synchronous approach to the design and implementation of reactive Real-Time system, the modular verification from the point of view of the refining program is best achieved with observers.

Electronic Notes in Theoretical Computer Science, 2006

Mathematical Foundations of Computer …, 1997

Action re nement in process algebras has been widely studied in the last few years as a means to support top-down design of systems. A speci c notion of re nement arises when a dependency relation on the actions (in the Mazurkiewicz sense) is used to control the inheritance of orderings from the abstract level. In this paper we present a rather simple operational semantics for dependency-based action re nement. We show the consistency of the operational with a (previously published) denotational semantics. We moreover show that bisimulation is a congruence for dependency-based re nement. Finally, we give an illustrative example.

1997

We review a number of temporal verification techniques for reactive systems using modularity and abstraction. Their use allows the verification of larger systems, and the incremental verification of systems as they are developed and refined. In particular, we show how deductive verification tools, and the combination of finite-state model checking and abstraction, allow the verification of infinite-state systems featuring data types commonly used in software specifications, including real-time and hybrid systems.

Formal Aspects of Computing, 1992

In this paper, we bring together the use of temporal logic for specifying concurrent systems, in the tradition initiated by A.Pnueli, and the use of tools from category theory as a means for structuring specifications as combinations of theories in the style developed by R.Burstall and J.Goguen. As a result, we obtain a framework in which systems of interconnected components can be described by assembling the specifications of their components around a diagram, using theory morphisms to specify how the components interact. This view of temporal theories as specification units naturally brings modularity to the description and analysis of systems. Moreover, it becomes possible to import into the area of formal development of reactive systems the wide body of specification techniques that have been defined for structuring specifications independently of the underlying logic, and that have been applied with great success in the area of Abstract Data Types. Finally, as a discipline of design, we use the object-oriented paradigm according to which components keep private data and interact by sharing actions, with a view towards providing formal tools for the specification of concurrent objects.

TAPSOFT'97: Theory and Practice of Software …, 1997

We propose a theory of process re nement which relates behavioural descriptions belonging to conceptually di erent abstraction levels, through a so-called vertical implementation relation. The theory is based on action re nement, which permits to relate abstract actions of the speci cation to concrete computations of the implementation it is developed in the standard interleaving approach. A number of proof rules is shown to be sound for the particular vertical implementation relation (based on observation congruence) we study in this paper. We give an illustrative example. Appeared in: TAPSOFT '97: Theory and Practice of Software Development, M. Bidoit and M. Dauchet (Eds.), pp. 772{786

Formal Aspects of Computing, 2008

Two styles of description arise naturally in formal specification: state-based and behavioural. In state-based notations, a system is characterised by a collection of variables, and their values determine which actions may occur throughout a system history. Behavioural specifications describe the chronologies of actions—interactions between a system and its environment. The exact nature of such interactions is captured in a variety of semantic models with corresponding notions of refinement; refinement in state based systems is based on the semantics of sequential programs and is modelled relationally. Acknowledging that these viewpoints are complementary, substantial research has gone into combining the paradigms. The purpose of this paper is to do three things. First, we survey recent results linking the relational model of refinement to the process algebraic models. Specifically, we detail how variations in the relational framework lead to relational data refinement being in corr...

IEEE Parallel & Distributed Technology: Systems & Applications, 1993

Computer Networks and ISDN Systems, 1993

A system is described which supports proofs of both behavioural and logical properties of concurrent systems; these are specified by means of a process algebra and its associated logics. The logic is an action based version of the branching time logic CTL which we call ACTL; it is interpreted over transition labelled structures while CTL is interpreted over state labelled ones. The core of the system are two existing tools, AUTO and EMC. The f'wst builds the labelled transition system corresponding to a term of a process algebra and permits proof of equivalence and simplification of terms, while the second chocks validity of CTL logical formulae. The integration is realized by memos of two translation functions from the action based branching time logic ACTL to CTL and from transition-labelled to state-labelled structures. The correctness of the integration is guaranteed by the proof that the two functions when coupled preserve satisfiability of logical formulae.