Gradient discretization of Hybrid Dimensional Darcy Flows in Fractured Porous Media with discontinuous pressures at the matrix fracture interfaces

We investigate the discretization of Darcy flow through fractured porous media on general meshes. We consider a hybrid dimensional model, invoking a complex network of planar fractures. The model accounts for matrix-fracture interactions and fractures acting either as drains or as barriers, i.e. we have to deal with pressure discontinuities at matrix-fracture interfaces. The numerical analysis is performed in the general framework of gradient discretizations which is extended to the model under consideration. Two families of schemes namely the Vertex Approximate Gradient scheme (VAG) and the Hybrid Finite Volume scheme (HFV) are detailed and shown to satisfy the gradient scheme framework, which yields, in particular, convergence. Numerical tests confirm the theoretical results. Gradient Discretization; Darcy Flow, Discrete Fracture Networks, Finite Volum

On the generation of equational dynamic logics for weighted imperative programs

Dynamic logic is a powerful framework for reasoning about imperative programs. This paper extends previous work [9] on the systematic generation of dynamic logics from the propositional to the equational case, to capture `full- edged' imperative programs. The generation process is parametric on a structure specifying a notion of `weight' assigned to programs. The paper introduces also a notion of bisimilarity on models of the generated logics, which is shown to entail modal equivalence with respect to the latter.POCI-01-0145-FEDER-030947. ERDF—European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT - Fundação para a Ciência e a Tecnologia, within project POCI-01-0145-FEDER-030947. The second author is supported in the scope of the framework contract foreseen in the numbers 4, 5 and 6 of the article 23, of the Decree-Law 57/2016, of August 29, changed by Portuguese Law 57/2017, of July 19 and by UID/MAT/04106/2019 at CIDM

Verification for Everyone? An Overview of Dynamic Logic

This note, reporting the homonym keynote presented in the International Symposium on Molecular Logic and Computational Synthetic Biology 2018, traces an informal roadmap on Dynamic Logic (DL) field, focusing on its versatility and resilience to be adjusted and adopted in a wide class of application domains and computational paradigms. The exposition argues the room for developments on tagging DL to the analysis of synthetic biologic domain.publishe

Extended ML: Past, present and future

An overview of past, present and future work on the Extended ML formal program development framework is given, with emphasis on two topics of current active research: the semantics of the Extended ML specification language, and tools to support formal program development

Testing data types implementations from algebraic specifications

Algebraic specifications of data types provide a natural basis for testing data types implementations. In this framework, the conformance relation is based on the satisfaction of axioms. This makes it possible to formally state the fundamental concepts of testing: exhaustive test set, testability hypotheses, oracle. Various criteria for selecting finite test sets have been proposed. They depend on the form of the axioms, and on the possibilities of observation of the implementation under test. This last point is related to the well-known oracle problem. As the main interest of algebraic specifications is data type abstraction, testing a concrete implementation raises the issue of the gap between the abstract description and the concrete representation. The observational semantics of algebraic specifications bring solutions on the basis of the so-called observable contexts. After a description of testing methods based on algebraic specifications, the chapter gives a brief presentation of some tools and case studies, and presents some applications to other formal methods involving datatypes

Role-Based Development of Dynamically Evolving Esembles

Part 1: Invited TalksInternational audienceAn ensemble is a set of computing entities that collaborate to perform a certain task. Typically an ensemble changes dynamically its constitution such that new members can join and other members can leave an ensemble during its execution. The members of an ensemble interact through message exchange. They are modelled as instances of certain role types which can be adopted by components of an underlying component system. We propose a dynamic logic to describe the evolution of ensembles from a global perspective. Using the power of dynamic logic with diamond and box modalities over regular expressions of actions (involving role instance creation, message exchange and component access) we can specify safety and liveness properties as well as desired and forbidden interaction scenarios. Thus our approach is suitable to write formal requirements specifications for ensemble behaviours. For ensemble design and implementation we propose ensemble realisations. An ensemble realisation takes a local view by giving a constructive specification for each single role type in terms of a process algebraic expression. Correctness of an ensemble realisation is defined semantically: its generated ensemble transition system must be a model of the requirements specification. We consider bisimulation of ensemble transition systems and show that our approach enjoys the Hennessy-Milner property