Graphical Verification of a Spatial Logic for the Graphical Verification of a Spatial Logic for the pi-calculus

The paper introduces a novel approach to the verification of spatial properties for finite [pi]-calculus specifications. The mechanism is based on a recently proposed graphical encoding for mobile calculi: Each process is mapped into a (ranked) graph, such that the denotation is fully abstract with respect to the usual structural congruence (i.e., two processes are equivalent exactly when the corresponding encodings yield the same graph). Spatial properties for reasoning about the behavior and the structure of pi-calculus processes are then expressed in a logic introduced by Caires, and they are verified on the graphical encoding of a process, rather than on its textual representation. More precisely, the graphical presentation allows for providing a simple and easy to implement verification algorithm based on the graphical encoding (returning true if and only if a given process verifies a given spatial formula)

Graphical Encoding of a Spatial Logic for the pi-Calculus

This paper extends our graph-based approach to the verification of spatial properties of π-calculus specifications. The mechanism is based on an encoding for mobile calculi where each process is mapped into a graph (with interfaces) such that the denotation is fully abstract with respect to the usual structural congruence, i.e., two processes are equivalent exactly when the corresponding encodings yield isomorphic graphs. Behavioral and structural properties of π-calculus processes expressed in a spatial logic can then be verified on the graphical encoding of a process rather than on its textual representation. In this paper we introduce a modal logic for graphs and define a translation of spatial formulae such that a process verifies a spatial formula exactly when its graphical representation verifies the translated modal graph formula

Towards an embedding of Graph Transformation in Intuitionistic Linear Logic

Linear logics have been shown to be able to embed both rewriting-based approaches and process calculi in a single, declarative framework. In this paper we are exploring the embedding of double-pushout graph transformations into quantified linear logic, leading to a Curry-Howard style isomorphism between graphs and transformations on one hand, formulas and proof terms on the other. With linear implication representing rules and reachability of graphs, and the tensor modelling parallel composition of graphs and transformations, we obtain a language able to encode graph transformation systems and their computations as well as reason about their properties

A Rewriting-Based Model Checker for the Linear Temporal Logic of Rewriting

AbstractThis paper presents a model checker for LTLR, a subset of the temporal logic of rewriting TLR* extending linear temporal logic with spatial action patterns. Both LTLR and TLR* are very expressive logics generalizing well-known state-based and action-based logics. Furthermore, the semantics of TLR* is given in terms of rewrite theories, so that the concurrent systems on which the LTLR properties are model checked can be specified at a very high level with rewrite rules. This paper answers a nontrivial challenge, namely, to be able to build a model checker to model check LTLR formulas on rewrite theories with relatively little effort by reusing Maudeʼs LTL model checker for rewrite theories. For this, the reflective features of both rewriting logic and its Maude implementation have proved extremely useful

Approches formelles pour l'analyse de la performabilité des systèmes communicants mobiles (Applications aux réseaux de capteurs sans fil)

Nous nous intéressons à l'analyse des exigences de performabilité des systèmes communicants mobiles par model checking. Nous modélisons ces systèmes à l'aide d'un formalisme de haut niveau issu du p-calcul, permettant de considérer des comportements stochastiques, temporels, déterministes, ou indéterministes. Cependant, dans le p-calcul, la primitive de communication de base des systèmes est la communication en point-à-point synchrone. Or, les systèmes mobiles, qui utilisent des réseaux sans fil, communiquent essentiellement par diffusion locale. C'est pourquoi, dans un premier temps, nous définissons la communication par diffusion dans le p-calcul, afin de mieux modéliser les systèmes que nous étudions. Nous proposons d'utiliser des versions probabilistes et stochastiques de l'algèbre que nous avons défini, pour permettre des études de performance. Nous en définissons une version temporelle permettant de considérer le temps dans les modèles. Mais l'absence d'outils d'analyse des propriétés sur des modèles spécifiés en une algèbre issue du p-calcul est un obstacle majeur à notre travail. La définition de règles de traduction en langage PRISM, nous permet de traduire nos modèles, en modèles de bas niveau supports du model checking, à savoir des chaînes de Markov à temps discret, à temps continu, des automates temporisés, ou des automates temporisés probabilistes. Nous avons choisi l'outil PRISM car, à notre connaissance, dans sa dernière version, il est le seul outil à supporter les formalismes de bas niveau que nous venons de citer, et ainsi il permet de réaliser des études de performabilité complètes. Cette façon de procéder nous permet de pallier à l'absence d'outils d'analyse pour nos modèles. Par la suite, nous appliquons ces concepts théoriques aux réseaux de capteurs sans fil mobiles.We are interested in analyzing the performability requirements of mobile communication systems by using model checking techniques. We model these systems using a high-level formalism derived from the p-calculus, for considering stochastic, timed, deterministic or indeterministic behaviors. However, in the p-calculus, the basic communication primitive of systems is the synchronous point-to-point communication. However, mobile systems that use wireless networks, mostly communicate by local broadcast. Therefore, we first define the broadcast communication into the p-calculus, to better model the systems we study. We propose to use probabilistic and stochastic versions of the algebra we have defined to allow performance studies. We define a temporal version to consider time in the models. But the lack of tools for analyzing properties of models specified with p-calculus is a major obstacle to our work and its objectives. The definition of translation rules into the PRISM language allows us to translate our models in low-level models which can support model checking, namely discrete time, or continuous time Markov chains, timed automata, or probabilistic timed automata. We chose the PRISM model checker because, in our best knowledge, in its latest version, it is the only tool that supports the low-level formalisms that we have previously cited, and thus, makes it possible to realize complete performability studies. This approach allows us to overcome the lack of model checkers for our models. Subsequently, we apply these theoretical concepts to analyse performability of mobile wireless sensor networks.PARIS-CNAM (751032301) / SudocSudocFranceF

Continuous-time temporal logic specification and verification for nonlinear biological systems in uncertain contexts

In this thesis we introduce a complete framework for modelling and verification of biological systems in uncertain contexts based on the bond-calculus process algebra and the LBUC spatio-temporal logic. The bond-calculus is a biological process algebra which captures complex patterns of interaction based on affinity patterns, a novel communication mechanism using pattern matching to express multiway interaction affinities and general kinetic laws, whilst retaining an agent-centric modelling style for biomolecular species. The bond-calculus is equipped with a novel continuous semantics which maps models to systems of Ordinary Differential Equations (ODEs) in a compositional way. We then extend the bond-calculus to handle uncertain models, featuring interval uncertainties in their species concentrations and reaction rate parameters. Our semantics is also extended to handle uncertainty in every aspect of a model, producing non-deterministic continuous systems whose behaviour depends either on time-independent uncertain parameters and initial conditions, corresponding to our partial knowledge of the system at hand, or time-varying uncertain inputs, corresponding to genuine variability in a system’s behaviour based on environmental factors. This language is then coupled with the LBUC spatio-temporal logic which combines Signal Temporal Logic (STL) temporal operators with an uncertain context operator which quantifies over an uncertain context model describing the range of environments over which a property must hold. We develop model-checking procedures for STL and LBUC properties based on verified signal monitoring over flowpipes produced by the Flow* verified integrator, including the technique of masking which directs monitoring for atomic propositions to time regions relevant to the overall verification problem at hand. This allows us to monitor many interesting nested contextual properties and frequently reduces monitoring costs by an order of magnitude. Finally, we explore the technique of contextual signal monitoring which can use a single Flow* flowpipe representing a functional dependency to complete a whole tree of signals corresponding to different uncertain contexts. This allows us to produce refined monitoring results over the whole space and to explore the variation in system behaviour in different contexts