A Multi-Core Solver for Parity Games

We describe a parallel algorithm for solving parity games,\ud with applications in, e.g., modal mu-calculus model\ud checking with arbitrary alternations, and (branching) bisimulation\ud checking. The algorithm is based on Jurdzinski's Small Progress\ud Measures. Actually, this is a class of algorithms, depending on\ud a selection heuristics.\ud \ud Our algorithm operates lock-free, and mostly wait-free (except for\ud infrequent termination detection), and thus allows maximum\ud parallelism. Additionally, we conserve memory by avoiding storage\ud of predecessor edges for the parity graph through strictly\ud forward-looking heuristics.\ud \ud We evaluate our multi-core implementation's behaviour on parity games\ud obtained from mu-calculus model checking problems for a set of\ud communication protocols, randomly generated problem instances, and\ud parametric problem instances from the literature.\ud \u

Benchmarks for Parity Games (extended version)

We propose a benchmark suite for parity games that includes all benchmarks that have been used in the literature, and make it available online. We give an overview of the parity games, including a description of how they have been generated. We also describe structural properties of parity games, and using these properties we show that our benchmarks are representative. With this work we provide a starting point for further experimentation with parity games.Comment: The corresponding tool and benchmarks are available from https://github.com/jkeiren/paritygame-generator. This is an extended version of the paper that has been accepted for FSEN 201

Obtaining Memory-Efficient Solutions to Boolean Equation Systems

AbstractThis paper is concerned with memory-efficient solution techniques for Boolean fixed-point equations. We show how certain structures of fixed-point equation systems, often encountered in solving verification problems, can be exploited in order to substantially improve the performance of fixed-point computations. Also, we investigate the space complexity of the problem of solving Boolean equation systems, showing a NL-hardness result. A prototype of the proposed technique has been implemented and experimental results on a series of protocol verification benchmarks are reported

Analysis of Boolean Equation Systems through Structure Graphs

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

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 Strategies for Datalog-based Points-To Analysis

During the last decade, several hard problems have been described and solved in Datalog in a sound way (points-to analyses, data web management, security, privacy, and trust). In this work, we describe novel evaluation strategies for this language within the context of program analyses. We first decompose any Datalog program into a program where rules have at most two atoms in their body. Then, we show that a specialized bottom-up evaluation algorithm with time and memory guarantees can be described as the on-the-fly resolution of a Boolean Equation System (Bes). The resolution computes all ground atoms in an efficient way thanks to a compact data structure with constant time access that has so far not been used in the Datalog or the Bes literature. A prototype has been developed and tested on a number of real Java projects in the context of Andersen’s points-to analysis. Experimental results show that our prototype is better than state-of-the-art solvers in terms of resolution time and memory consumption

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

On-the-Fly Model Checking for Extended Action-Based Probabilistic Operators

International audienceThe quantitative analysis of concurrent systems requires expressive and user-friendly property languages combining temporal, data-handling, and quantitative aspects. In this paper, we aim at facilitating the quantitative analysis of systems modeled as PTSs (Probabilistic Transition Systems) labeled by actions containing data values and probabilities. We propose a new regular probabilistic operator that computes the probability measure of a path specified by a generalized regular formula involving arbitrary computations on data values. This operator, which subsumes the Until operators of PCTL and their action-based counterparts, can provide useful quantitative information about paths having certain (e.g., peak) cost values. We integrated the regular probabilistic operator into MCL (Model Checking Language) and we devised an associated on-the-fly model checking method, based on a combined local resolution of linear and Boolean equation systems. We implemented the method in the EVALUATOR model checker of the CADP toolbox and experimented it on realistic PTSs modeling concurrent systems

LTSmin: high-performance language-independent model checking

In recent years, the LTSmin model checker has been extended with support for several new modelling languages, including probabilistic (Mapa) and timed systems (Uppaal). Also, connecting additional language front-ends or ad-hoc state-space generators to LTSmin was simplified using custom C-code. From symbolic and distributed reachability analysis and minimisation, LTSmin’s functionality has developed into a model checker with multi-core algorithms for on-the-fly LTL checking with partial-order reduction, and multi-core symbolic checking for the modal μ calculus, based on the multi-core decision diagram package Sylvan.\ud In LTSmin, the modelling languages and the model checking algorithms are connected through a Partitioned Next-State Interface (Pins), that allows to abstract away from language details in the implementation of the analysis algorithms and on-the-fly optimisations. In the current paper, we present an overview of the toolset and its recent changes, and we demonstrate its performance and versatility in two case studies