Model Checking for Nominal Calculi

Abstract

Abstract. Nominal calculi have been shown very effective to formally model a variety of computational phenomena. The models of nominal calculi have often infinite states, thus making model checking a difficult task. In this note we survey some of the approaches for model checking nominal calculi. Then, we focus on History-Dependent automata, a syntax-free automaton-based model of mobility. History-Dependent automata have provided the formal basis to design and implement some existing verification toolkits. We then introduce a novel syntax-free setting to model the symbolic semantics of a nominal calculus. Our approach relies on the notions of reactive systems and observed borrowed contexts introduced by Leifer and Milner, and further developed by Sassone, Lack and Sobocinski. We argue that the symbolic semantics model based on borrowed contexts can be conveniently applied to web service discovery and binding. SummaryModel checking has been shown very effective for proving properties of system behaviour whenever a finite model of it can be constructed. The approach is convenient since it does not require formal proofs and since the same automaton-like model can accommodate system specification languages with substantially different syntax and semantics. Among the properties which can be checked, behavioural equivalence is especially important for matching specifications and implementations, for proving the system resistant to certain attacks and for replacing the system with a simpler one with the same properties.Names have been used in process calculi for representing a variety of different informations concerning addresses, mobility links, continuations, localities, causal dependencies, security keys and session identifiers. When an unbound number of new names can be generated during execution, the models tend to be infinite even in the simplest cases, unless explicit mechanisms are introduced to allocate and garbage collect names, allowing the same states to be reused with different name meanings.We review some existing syntax-free models for name-passing calculi and focus on History-Dependent automata (HD-automata), introduced by Montanari and Pistore in 1995 [62]. 63,71] have been shown a suitable automata-based model for representing Petri nets, CCS with causality and localities and some versions of π-calculus [59,75].

Event based choreography

“…4). Moreover, bisimulation-checking techniques such as those of [24] could be employed to semi-automatically verify finite-state designs.…”

Model checking processes specified in join-calculus algebra

“…Advances in model checking methodologies allow the verification of systems of considerable sizes [15] which make the verification effective in practice. The authors of [9] developed a methodology similar to the one described in this paper, where a nominal calculus is represented by history dependent automata and is model checked using software tools.…”

Fresh-register automata

“…permutation of fresh names. The stream of research on HD-automata has focussed both on foundational issues [17,22] and on pragmatic applications [7]. The work presented here shares objectives with HD-automata, and to some extent can be viewed as a complementary attempt to the same question, albeit based on basic machines of "first principles".…”

“…7 However, the usual (symbolic) notion of bisimulation between FRA's is not appropriate because it is defined for single-step transitions and, moreover, does not take into account the distinction between inputs and outputs. We therefore define the following notion.…”