Abstraction in parameterised Boolean equation systems

We present a general theory of abstraction for a variety of verification problems. Our theory is set in the framework of parameterized Boolean equation systems. The power of our abstraction theory is compared to that of generalised Kripke modal transition systems (GTSs). We show that for model checking the modal µ-calculus, our abstractions can be exponentially more succinct than GTSs and our theory is as complete as the GTS framework for abstraction. Furthermore, we investigate the completeness of our theory for verification problems other than the modal µ-calculus. We illustrate the potential of our theory through case studies using the first-order modal µ-calculus and a real-time extension thereof, conducted using a prototype implementation of a new syntactic transformation for equation systems

Parameterised model checking of probabilistic multi-agent systems

Swarm robotics has been put forward as a method of addressing a number of scenarios where scalability and robustness are desired. In order to deploy robotic swarms in safety-critical situations, it is necessary to verify their behaviour. Model checking gives a possible approach to do this; however, with traditional model checking techniques only systems of a finite size can be considered. This presents an issue for swarm systems, where the number of participants in the system is not known at design-time and may be arbitrarily large. To overcome this, parameterised model checking (PMC) techniques have been developed which enable the verification of systems where the number of participants is not known until run-time. However, protocols followed by robotic swarms are often stochastic in nature, and this cannot be modelled with current PMC techniques. This is the gap that this thesis aims to overcome. In particular, two parameterised semantics for reasoning about multi-agent systems are extended to incorporate probabilities. One of these semantics is synchronous, whilst the other is interleaved. Abstract models which overapproximate the systems being considered are constructed using counter abstraction techniques. These abstract models are used to develop parameterised verification procedures for a number of specification logics on both bounded and unbounded traces. The decision procedures presented are shown to be sound, and in some cases also complete. Further, the techniques are extended to allow modelling of situations where agents may exhibit faulty behaviour, as well as scenarios where the strategic capabilities of the participants needs to be verified. The procedures are all implemented in a novel verification toolkit called PSV (Probabilistic Swarm Verifier), built on top of the probabilistic model checker PRISM. This toolkit is used to verify three case studies from both swarm robotics and other application domains.Open Acces

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

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

Searching for a Solution to Program Verification=Equation Solving in CCS

International audienceUnder non-exponential discounting, we develop a dynamic theory for stopping problems in continuous time. Our framework covers discount functions that induce decreasing impatience. Due to the inherent time inconsistency, we look for equilibrium stopping policies, formulated as fixed points of an operator. Under appropriate conditions, fixed-point iterations converge to equilibrium stopping policies. This iterative approach corresponds to the hierarchy of strategic reasoning in game theory and provides “agent-specific” results: it assigns one specific equilibrium stopping policy to each agent according to her initial behavior. In particular, it leads to a precise mathematical connection between the naive behavior and the sophisticated one. Our theory is illustrated in a real options model