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Gières, France

Dang T.,French National Center for Scientific Research | Maler O.,French National Center for Scientific Research | Testylier R.,VERIMAG
HSCC'10 - Proceedings of the 13th ACM International Conference on Hybrid Systems: Computation and Control

This paper is concerned with reachable set computation for non-linear systems using hybridization. The essence of hybridization is to approximate a non-linear vector field by a simpler (such as affine) vector field. This is done by partitioning the state space into small regions within each of which a simpler vector field is defined. This approach relies on the availability of methods for function approximation and for handling the resulting dynamical systems. Concerning function approximation using interpolation, the accuracy depends on the shapes and sizes of the regions which can compromise as well the speed of reachability computation since it may generate spurious classes of trajectories. In this paper we study the relationship between the region geometry and reachable set accuracy and propose a method for constructing hybridization regions using tighter interpolation error bounds. In addition, our construction exploits the dynamics of the system to adapt the orientation of the regions, in order to achieve better time-efficiency. We also present some experimental results on a high-dimensional biological system, to demonstrate the performance improvement. © 2010 ACM. Source

Sifakis J.,VERIMAG
Proceedings -Design, Automation and Test in Europe, DATE

Traditional engineering disciplines such as civil or mechanical engineering are based on solid theory for building artefacts with predictable behavior over their lifetime. In contrast, we lack similar constructivity results for computing systems engineering: computer science provides only partial answers to particular system design problems. With few exceptions, predictability is impossible to guarantee at design time and therefore, a posteriori verification remains the only means for ensuring their correct operation. © 2011 EDAA. Source

Gawlitza T.M.,VERIMAG | Seidl H.,TU Munich
ACM Transactions on Programming Languages and Systems

We present practical algorithms for computing exact least solutions of equation systems over the reals with addition, multiplication by positive constants, minimum and maximum. The algorithms are based on strategy iteration. Our algorithms can, for instance, be used for the analysis of recursive stochastic games. In the present article we apply our techniques for computing abstract least fixpoint semantics of affine programs over the relational template polyhedra domain. In particular, we thus obtain practical algorithms for computing abstract least fixpoint semantics over the abstract domains of intervals, zones, and octagons. © 2011 ACM. Source

Pavlinovic Z.,New York University | King T.,VERIMAG | Wies T.,New York University
Proceedings of the ACM SIGPLAN International Conference on Functional Programming, ICFP

Compilers for statically typed functional programming languages are notorious for generating confusing type error messages. When the compiler detects a type error, it typically reports the program location where the type checking failed as the source of the error. Since other error sources are not even considered, the actual root cause is often missed. A more adequate approach is to consider all possible error sources and report the most useful one subject to some usefulness criterion. In our previous work, we showed that this approach can be formulated as an optimization problem related to satisfiability modulo theories (SMT). This formulation cleanly separates the heuristic nature of usefulness criteria from the underlying search problem. Unfortunately, algorithms that search for an optimal error source cannot directly use principal types which are crucial for dealing with the exponential-time complexity of the decision problem of polymorphic type checking. In this paper, we present a new algorithm that efficiently finds an optimal error source in a given ill-typed program. Our algorithm uses an improved SMT encoding to cope with the high complexity of polymorphic typing by iteratively expanding the typing constraints from which principal types are derived. The algorithm preserves the clean separation between the heuristics and the actual search. We have implemented our algorithm for OCaml. In our experimental evaluation, we found that the algorithm reduces the running times for optimal type error localization from minutes to seconds and scales better than previous localization algorithms. © 2015 ACM. Source

von Essen C.,VERIMAG | Giannakopoulou D.,NASA
International Journal on Software Tools for Technology Transfer

The next generation airborne collision avoidance system, ACAS X, departs from the traditional deterministic model on which the current system, TCAS, is based. To increase robustness, ACAS X relies on probabilistic models to represent the various sources of uncertainty. The work reported in this paper identifies verification challenges for ACAS X, and studies the applicability of probabilistic verification and synthesis techniques in addressing these challenges. Due to shortcomings of off-the-shelf probabilistic analysis tools, we developed a new framework, named VeriCA (Verification for Collision Avoidance). VeriCA is a combined probabilistic synthesis and verification framework that is custom designed for ACAS X and systems with similar characteristics. VeriCA supports Java as a modeling language, is memory efficient, employs parallelization, and provides an interactive simulator that displays aircraft encounters and the corresponding ACAS X behavior. We describe the application of our framework to ACAS X, together with the results and recommendations that our analysis produced. © 2015 Springer-Verlag Berlin Heidelberg (outside the USA) Source

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