Efficient Instantiation of Parameterised Boolean Equation Systems to Parity Games

Parameterised Boolean Equation Systems (PBESs) are sequences of Boolean fixed point equations with data variables, used for, e.g., verification of modal μ-calculus formulae for process algebraic specifications with data. Solving a PBES is usually done by instantiation to a Parity Game and then solving the game. Practical game solvers exist, but the instantiation step is the bottleneck. We enhance the instantiation in two steps. First, we transform the PBES to a Parameterised Parity Game (PPG), a PBES with each equation either conjunctive or disjunctive. Then we use LTSmin, that offers transition caching, efficient storage of states and both distributed and symbolic state space generation, for generating the game graph. To that end we define a language module for LTSmin, consisting of an encoding of variables with parameters into state vectors, a grouped transition relation and a dependency matrix to indicate the dependencies between parts of the state vector and transition groups. Benchmarks on some large case studies, show that the method speeds up the instantiation significantly and decreases memory usage drastically

Generating and Solving Symbolic Parity Games

We present a new tool for verification of modal mu-calculus formulae for process specifications, based on symbolic parity games. It enhances an existing method, that first encodes the problem to a Parameterised Boolean Equation System (PBES) and then instantiates the PBES to a parity game. We improved the translation from specification to PBES to preserve the structure of the specification in the PBES, we extended LTSmin to instantiate PBESs to symbolic parity games, and implemented the recursive parity game solving algorithm by Zielonka for symbolic parity games. We use Multi-valued Decision Diagrams (MDDs) to represent sets and relations, thus enabling the tools to deal with very large systems. The transition relation is partitioned based on the structure of the specification, which allows for efficient manipulation of the MDDs. We performed two case studies on modular specifications, that demonstrate that the new method has better time and memory performance than existing PBES based tools and can be faster (but slightly less memory efficient) than the symbolic model checker NuSMV.Comment: In Proceedings GRAPHITE 2014, arXiv:1407.767

Datalog-Based program analysis with BES and RWL

This paper describes two techniques for Datalog query evaluation and their application to object-oriented program analysis. The first technique transforms Datalog programs into an implicit Boolean Equation System (Bes) that can then be solved by using linear-time complexity algorithms that are available in existing, general purpose verification toolboxes such as Cadp. In order to improve scalability and to enable analyses involving advanced meta-programming features, we develop a second methodology that transforms Datalog programs into rewriting logic (Rwl) theories. This method takes advantage of the preeminent features and facilities that are available within the high-performance system Maude, which provides a very efficient implementation of Rwl. We provide evidence of the practicality of both approaches by reporting on some experiments with a number of real-world Datalog-based analyses. © 2011 Springer-Verlag.This work has been partially supported by the eu(feder), the Spanish mec/micinn under grants tin2007-68093-C02 and tin2010-21062-C02-02, and the Generalitat Valenciana under grant Emergentes gv/2009/024. M.A.Feliu was partially supported by the Spanish mec fpu grant AP2008-00608.Alpuente Frasnedo, M.; Feliú Gabaldón, MA.; Joubert, C.; Villanueva García, A. (2011). Datalog-Based program analysis with BES and RWL. En Datalog Reloaded. Springer Verlag (Germany). 6702:1-20. https://doi.org/10.1007/978-3-642-24206-9_1S1206702Afrati, F.N., Ullman, J.D.: Optimizing joins in a map-reduce environment. In: Manolescu, I., Spaccapietra, S., Teubner, J., Kitsuregawa, M., Léger, A., Naumann, F., Ailamaki, A., Özcan, F. (eds.) EDBT. ACM International Conference Proceeding Series, vol. 426, pp. 99–110. 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Evaluation of Datalog queries and its application to the static analysis of Java code

Two approaches for evaluating Datalog programs are presented: one based on boolean equation systems, and the other based on rewriting logic. The work is presented in the context of the static analysis of Java programs specified in Datalog.Feliú Gabaldón, MA. (2010). Evaluation of Datalog queries and its application to the static analysis of Java code. http://hdl.handle.net/10251/14016Archivo delegad

SCOOP: A Tool for SymboliC Optimisations Of Probabilistic Processes

This paper presents SCOOP: a tool that symbolically optimises process-algebraic specifications of probabilistic processes. It takes specifications in the prCRL language (combining data and probabilities), which are linearised first to an intermediate format: the LPPE. On this format, optimisations such as dead-variable reduction and confluence reduction are applied automatically by SCOOP. That way, drastic state space reductions are achieved while never having to generate the complete state space, as data variables are unfolded only locally. The optimised state spaces are ready to be analysed by for instance CADP or PRISM

Logic-based techniques for program analysis and specification synthesis

La Tesis investiga técnicas ágiles dentro del paradigma declarativo para dar solución a dos problemas: el análisis de programas y la inferencia de especificaciones a partir de programas escritos en lenguajes multiparadigma y en lenguajes imperativos con tipos, objetos, estructuras y punteros. Respecto al estado actual de la tesis, la parte de análisis de programas ya está consolidada, mientras que la parte de inferencia de especificaciones sigue en fase de desarrollo activo. La primera parte da soluciones para la ejecución de análisis de punteros especificados en Datalog. En esta parte se han desarrollado dos técnicas de ejecución de especificaciones en dicho lenguaje Datalog: una de ellas utiliza resolutores de sistemas de ecuaciones booleanas, y la otra utiliza la lógica de reescritura implementada eficientemente en el lenguaje Maude. La segunda parte desarrolla técnicas de inferencia de especificaciones a partir de programas. En esta parte se han desarrollado dos métodos de inferencia de especificaciones. El primer método se desarrolló para el lenguaje lógico-funcional Curry y permite inferir especificaciones ecuacionales mediante interpretación abstracta de los programas. El segundo método está siendo desarrollado para lenguajes imperativos realistas, y se ha aplicado a un subconjunto del lenguaje de programación C. Este método permite inferir especificaciones en forma de reglas que representan las distintas relaciones entre las propiedades que el estado de un programa satisface antes y después de su ejecución. Además, estas propiedades son expresables en términos de las abstracciones funcionales del propio programa, resultando en una especificación de muy alto nivel y, por lo tanto, de más fácil comprensión.Feliú Gabaldón, MA. (2013). Logic-based techniques for program analysis and specification synthesis [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/33747TESI

A linear process algebraic format for probabilistic systems with data

This paper presents a novel linear process algebraic format for probabilistic automata. The key ingredient is a symbolic transformation of probabilistic process algebra terms that incorporate data into this linear format while preserving strong probabilistic bisimulation. This generalises similar techniques for traditional process algebras with data, and — more importantly — treats data and data-dependent probabilistic choice in a fully symbolic manner, paving the way to the symbolic analysis of parameterised probabilistic systems