128 research outputs found

    Checking bisimilarity for attributed graph transformation

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    Borrowed context graph transformation is a technique developed by Ehrig and Koenig to define bisimilarity congruences from reduction semantics defined by graph transformation. This means that, for instance, this technique can be used for defining bisimilarity congruences for process calculi whose operational semantics can be defined by graph transformation. Moreover, given a set of graph transformation rules, the technique can be used for checking bisimilarity of two given graphs. Unfortunately, we can not use this ideas to check if attributed graphs are bisimilar, i.e. graphs whose nodes or edges are labelled with values from some given data algebra and where graph transformation involves computation on that algebra. The problem is that, in the case of attributed graphs, borrowed context transformation may be infinitely branching. In this paper, based on borrowed context transformation of what we call symbolic graphs, we present a sound and relatively complete inference system for checking bisimilarity of attributed graphs. In particular, this means that, if using our inference system we are able to prove that two graphs are bisimilar then they are indeed bisimilar. Conversely, two graphs are not bisimilar if and only if we can find a proof saying so, provided that we are able to prove some formulas over the given data algebra. Moreover, since the proof system is complex to use, we also present a tableau method based on the inference system that is also sound and relatively complete.Postprint (published version

    Borrowed contexts for attributed graphs

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    Borrowed context graph transformation is a simple and powerful technique developed by Ehrig and König that allow us to derive labeled transitions and bisimulation congruences for graph transformation systems or, in general, for pocess calculi that can be defined in terms of graph transformation systems. Moreover, the same authors have also shown how to use this technique for the verification of bisimilarity. In principle, the main results about borrowed context transformation do not apply only to plain graphs, but they are generic in the sense that they apply to all categories tha satisfy certain properties related to the notion of adhesivity. In particular, this is the case of attributed graphs. However, as we show in the paper, the techniques used for checking bisimilarity are not equally generic and, in particular they fail, if we want to apply them to attributed graphs. To solve this problem, in this paper, we define a special notion of symbolic graph bisimulation and show how it can be used to check bisimilarity of attributed graphs.Postprint (published version

    Analysis of Boolean Equation Systems through Structure Graphs

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    We analyse the problem of solving Boolean equation systems through the use of structure graphs. The latter are obtained through an elegant set of Plotkin-style deduction rules. Our main contribution is that we show that equation systems with bisimilar structure graphs have the same solution. We show that our work conservatively extends earlier work, conducted by Keiren and Willemse, in which dependency graphs were used to analyse a subclass of Boolean equation systems, viz., equation systems in standard recursive form. We illustrate our approach by a small example, demonstrating the effect of simplifying an equation system through minimisation of its structure graph

    Bisimulations on data graphs

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    Bisimulation provides structural conditions to characterize indistinguishability from an external observer between nodes on labeled graphs. It is a fundamental notion used in many areas, such as verification, graph-structured databases, and constraint satisfaction. However, several current applications use graphs where nodes also contain data (the so called “data graphs”), and where observers can test for equality or inequality of data values (e.g., asking the attribute ‘name’ of a node to be different from that of all its neighbors). The present work constitutes a first investigation of “data aware” bisimulations on data graphs. We study the problem of computing such bisimulations, based on the observational indistinguishability for XPath —a language that extends modal logics like PDL with tests for data equality— with and without transitive closure operators. We show that in general the problem is PSPACE-complete, but identify several restrictions that yield better complexity bounds (CO- NP, PTIME) by controlling suitable parameters of the problem, namely the amount of non-locality allowed, and the class of models considered (graphs, DAGs, trees). In particular, this analysis yields a hierarchy of tractable fragments.Fil: Abriola, Sergio Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación En Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación En Ciencias de la Computacion; ArgentinaFil: Barceló, Pablo. Universidad de Chile; ChileFil: Figueira, Diego. Centre National de la Recherche Scientifique; FranciaFil: Figueira, Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación En Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación En Ciencias de la Computacion; Argentin

    Structural Analysis of Boolean Equation Systems

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    We analyse the problem of solving Boolean equation systems through the use of structure graphs. The latter are obtained through an elegant set of Plotkin-style deduction rules. Our main contribution is that we show that equation systems with bisimilar structure graphs have the same solution. We show that our work conservatively extends earlier work, conducted by Keiren and Willemse, in which dependency graphs were used to analyse a subclass of Boolean equation systems, viz., equation systems in standard recursive form. We illustrate our approach by a small example, demonstrating the effect of simplifying an equation system through minimisation of its structure graph

    Advanced reduction techniques for model checking

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    Improved verification methods for concurrent systems

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    ІНСЕРЦІЙНЕ МОДЕЛЮВАННЯ В ПРОЕКТУВАННІ РОЗПОДІЛЕНИХ СИСТЕМ. \ud INSERTION MODELING IN DISTRIBUTED SYSTEM DESIGN

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    Стаття описує методологію інсерційного моделювання, її реалізацію та застосування. Інсерційне моделювання являє собою методологію проектування розподілених систем, що управляється моделлю. Ця методологія базується на теорії взаємодіючих агентів та середовищ [1-2] та використовує Basic Protocol Specification Language (BPSL) для представлення специфікацій вимог до розподілених систем. [3-6]. Діаграма Послідовності з пре- та пост-умовами (логічними формулами, що інтерпретуються відповідно до опису середовища) – Базовий Протокол є центральним поняттям цієї мови. Семантика BPSL дозволяє конкретні та абстракті моделі рівних рівнів абстрактності. Моделі визначені як Basic Protocol Specifications (BPS) можуть у подальшому бути використані як для верифікація специфікацій вимог та і для генерації тестових наборів.\ud Інсерційне моделювання підтримується системою VRS (Verification of Requirement Specifications), створеною для компанії Моторола київською групою VRS у співробітництві із ЗАТ Моторола-Санкт-Петербург. Система дозволяє статичний аналіз вимог на основі автоматичного доведення теорем, символьної та дедуктивної перевірки моделей та породження трас для тестування із заданими критеріями покриття. Всі засоби були розроблені на базі формальної семантики BPSL, побудованої відповідно до методології інсерційного моделювання VRS була успішно застосована у великій кількості індустріальних проектів із різних галузей, включаючи телекомунікації, телематику та системи реального часу.----------------------------------\ud The paper describes insertion modeling methodology, its implementation and applications. Insertion modeling is a methodology of model driven distributed system design. It is based on the model of interaction of agents and environments [1-2] and use Basic Protocol Specification Language (BPSL) for the representation of requirement specifications of distributed systems [3-6]. The central notion of this language is the notion of basic protocol – a sequencing diagram with pre- and postconditions, logic formulas interpreted by environment description. Semantics of BPSL allows concrete and abstract models on different levels of abstraction. Models defined by Basic Protocol Specifications (BPS) can be used for verification of requirement specifications as well as for generation of test cases for testing products, developed on the basis of BPS. \ud Insertion modeling is supported by the system VRS (Verification of Requirement Specifications), developed for Motorola by Kiev VRS group in cooperation with Motorola GSG Russia. The system provides static requirement checking on the base of automatic theorem proving, symbolic and deductive model checking, and generation of traces for testing with different coverage criteria. All tools have been developed on a base of formal semantics of BPSL constructed according to insertion modeling methodology. \ud The VRS has been successfully applied to a number of industrial projects from different domains including Telecommunications, Telematics and real time applications.\ud \u
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