Comparing refinements for failure and bisimulation semantics

FM 2009: Formal Methods, 2009

Transition rules with negative premises are needed in the structural operational semantics of programming and specification constructs such as priority and interrupt, as well as in timed extensions of specification languages. The well-known proof-theoretic semantics for transition system specifications involving such rules is based on wellsupported proofs for closed transitions. Dealing with open formulae by considering all closed instances is inherently non-modular -proofs are not necessarily preserved by disjoint extensions of the transition system specification.

Formal aspects of computing, 2006

This paper presents a new strand of investigation which complements our previous investigation of refinement for specifications whose semantics is given by partial relations (using Z as a linguistic vehicle for this semantics). It revolves around extending our mathematical apparatus so as to continue our quest for examining mathematically the essence of the lifted-totalisation semantics (which underlies the de facto standard notion of refinement in Z) and the role of the semantic elements ⊥ in model-theoretic refinement, but this time in the abortive paradigm. The analysis is given in two salient parts. In the first part, we consider the simpler framework of operation-refinement: we examine the (de facto) standard account of operation-refinement in this regime by introducing a simpler, normative theory which captures the notion of firing-conditions refinement directly in the language and in terms of the natural properties of preconditions and postconditions. In the second part, we generalise our analysis to a more intricate investigation of simulation-based data-refinement. The proof-theoretic approach we undertake in the formal analysis provides us with a mathematical apparatus which enables us to examine precisely the relationships amongst the various theories of refinement. This enables us to examine the general mathematical role that the ⊥ values play in model-theoretic refinement in the abortive paradigm, as well as the significance of the unique interaction of these values with the notions of lifting (of data simulations) and lifted-totalisation (of operations) in this regime. Furthermore, we generalise this mathematical analysis to a more conceptual one which also involves extreme specifications.

2002

We propose a methodology for the analysis of open systems based on process calculi and bisimilarity. Open systems are seen as coordinators (ie terms with place-holders), that evolve when suitable components (ie closed terms) fill in their place-holders. The distinguishing feature of our approach is the definition of a symbolic operational semantics for coordinators that exploits spatial/modal formulae as labels of transitions and avoids the universal closure of coordinators wrt all components.

Information and Computation, 2009

Bisimulations up-to Simulations up-to Canonical preorder Linear time-branching time spectrum We define (bi)simulations up-to a preorder and show how we can use them to provide a coinductive, (bi)simulation-like, characterisation of semantic (equivalences) preorders for processes. In particular, we can apply our results to all the semantics in the linear timebranching time spectrum that are defined by preorders coarser than the ready simulation preorder. The relation between bisimulations up-to and simulations up-to allows us to find some new relations between the equivalences that define the semantics and the corresponding preorders. In particular, we have shown that the simulation up-to an equivalence relation is a canonical preorder whose kernel is the given equivalence relation. Since all of these canonical preorders are defined in an homogeneous way, we can prove properties for them in a generic way. As an illustrative example of this technique, we generate an axiomatic characterisation of each of these canonical preorders, that is obtained simply by adding a single axiom to the axiomatization of the original equivalence relation. Thus we provide an alternative axiomatization for any axiomatizable preorder in the linear time-branching time spectrum, whose correctness and completeness can be proved once and for all. Although we first prove, by induction, our results for finite processes, then we see, by using continuity arguments, that they are also valid for infinite (finitary) processes.

Information Processing Letters, 1997

Electronic Notes in Theoretical Computer Science, 1998

Event structures have come to play an important role in the formal study of the behaviour of distributed systems. The advantage of event structures is that they explicitly exhibit the interplay between concurrency and nondeterminism. This paper is contributed to develop a numberof new bisimulations which are natural and nicely t with the concept of event structures. We establish closed relationships between the bisimulations, resulting in a lattice of implications. Some logics with a C T L avour, beinginterpreted over event structures, are further introduced to characterize the proposed bisimulations logically.

2012

We present a format for the specification of probabilistic transition systems that guarantees that bisimulation equivalence is a congruence for any operator defined in this format. In this sense, the format is somehow comparable to the ntyft/ntyxt format in a non-probabilistic setting. We also study the modular construction of probabilistic transition systems specifications and prove that some standard conservative extension theorems also hold in our setting. Finally, we show that the trace congruence for image-finite processes induced by our format is precisely bisimulation on probabilistic systems.

Lecture Notes in Computer Science, 1993

Information Processing Letters, 1991