Using non-convex approximations for efficient analysis of timed automata

The reachability problem for timed automata asks if there exists a path from an initial state to a target state. The standard solution to this problem involves computing the zone graph of the automaton, which in principle could be infinite. In order to make the graph finite, zones are approximated using an extrapolation operator. For reasons of efficiency in current algorithms extrapolation of a zone is always a zone and in particular it is convex. In this paper, we propose to solve the reachability problem without such extrapolation operators. To ensure termination, we provide an efficient algorithm to check if a zone is included in the so called region closure of another. Although theoretically better, closure cannot be used in the standard algorithm since a closure of a zone may not be convex. An additional benefit of the proposed approach is that it permits to calculate approximating parameters on-the-fly during exploration of the zone graph, as opposed to the current methods which do it by a static analysis of the automaton prior to the exploration. This allows for further improvements in the algorithm. Promising experimental results are presented.Comment: Extended version of FSTTCS 2011 pape

Algorithmic Verification of Continuous and Hybrid Systems

We provide a tutorial introduction to reachability computation, a class of computational techniques that exports verification technology toward continuous and hybrid systems. For open under-determined systems, this technique can sometimes replace an infinite number of simulations.Comment: In Proceedings INFINITY 2013, arXiv:1402.661

Better abstractions for timed automata

We consider the reachability problem for timed automata. A standard solution to this problem involves computing a search tree whose nodes are abstractions of zones. These abstractions preserve underlying simulation relations on the state space of the automaton. For both effectiveness and efficiency reasons, they are parametrized by the maximal lower and upper bounds (LU-bounds) occurring in the guards of the automaton. We consider the aLU abstraction defined by Behrmann et al. Since this abstraction can potentially yield non-convex sets, it has not been used in implementations. We prove that aLU abstraction is the biggest abstraction with respect to LU-bounds that is sound and complete for reachability. We also provide an efficient technique to use the aLU abstraction to solve the reachability problem.Comment: Extended version of LICS 2012 paper (conference paper till v6). in Information and Computation, available online 27 July 201

TCTL model checking of Time Petri Nets

International audienceIn this paper, we consider \emph{subscript} TCTL for Time Petri Nets (TPN-TCTL) for which temporal operators are extended with a time interval, specifying a time constraint on the firing sequences. We prove that the model-checking of a TPN-TCTL formula on a bounded TPN is decidable and is a PSPACE-complete problem. We propose a zone based state space abstraction that preserves marking reachability and traces of the TPN. As for Timed Automata (TA), the abstraction may use an over-approximation operator on zones to enforce the termination. A coarser (and efficient) abstraction is then provided and proved exact w.r.t. marking reachability and traces (LTL properties). Finally, we consider a subset of TPN-TCTL properties for which it is possible to propose efficient on-the-fly model-checking algorithms. Our approach consists in computing and exploring the zone based state space abstractio

Dynamic Partitioning in Linear Relation Analysis. Application to the Verification of Synchronous Programs

We apply linear relation analysis [CH78, HPR97] to the verificationof declarative synchronous programs [Hal98]. In this approach,state partitioning plays an important role: on one hand the precision of the results highly depends on the fineness of the partitioning; on the other hand, a too much detailed partitioning may result in an exponential explosion of the analysis. In this paper we propose to consider very general partitions of the state space and to dynamically select a suitable partitioning according to the property to be proved. The presented approach is quite general and can be applied to other abstract interpretations.Keywords and Phrases: Abstract Interpretation, Partitioning,Linear Relation Analysis, Reactive Systems, Program Verificatio

A Forward Reachability Algorithm for Bounded Timed-Arc Petri Nets

Timed-arc Petri nets (TAPN) are a well-known time extension of the Petri net model and several translations to networks of timed automata have been proposed for this model. We present a direct, DBM-based algorithm for forward reachability analysis of bounded TAPNs extended with transport arcs, inhibitor arcs and age invariants. We also give a complete proof of its correctness, including reduction techniques based on symmetries and extrapolation. Finally, we augment the algorithm with a novel state-space reduction technique introducing a monotonic ordering on markings and prove its soundness even in the presence of monotonicity-breaking features like age invariants and inhibitor arcs. We implement the algorithm within the model-checker TAPAAL and the experimental results document an encouraging performance compared to verification approaches that translate TAPN models to UPPAAL timed automata.Comment: In Proceedings SSV 2012, arXiv:1211.587

Verification and Control of Partially Observable Probabilistic Real-Time Systems

We propose automated techniques for the verification and control of probabilistic real-time systems that are only partially observable. To formally model such systems, we define an extension of probabilistic timed automata in which local states are partially visible to an observer or controller. We give a probabilistic temporal logic that can express a range of quantitative properties of these models, relating to the probability of an event's occurrence or the expected value of a reward measure. We then propose techniques to either verify that such a property holds or to synthesise a controller for the model which makes it true. Our approach is based on an integer discretisation of the model's dense-time behaviour and a grid-based abstraction of the uncountable belief space induced by partial observability. The latter is necessarily approximate since the underlying problem is undecidable, however we show how both lower and upper bounds on numerical results can be generated. We illustrate the effectiveness of the approach by implementing it in the PRISM model checker and applying it to several case studies, from the domains of computer security and task scheduling