Model checking polygonal differential inclusions using invariance kernels

Polygonal hybrid systems are a subclass of planar hybrid automata which can be represented by piecewise constant differential inclusions. Here, we identify and compute an important object of such systems’ phase portrait, namely invariance kernels. An invariant set is a set of initial points of trajectories which keep rotating in a cycle forever and the invariance kernel is the largest of such sets. We show that this kernel is a non-convex polygon and we give a non-iterative algorithm for computing the coordinates of its vertices and edges. Moreover, we present a breadth-first search algorithm for solving the reachability problem for such systems. Invariance kernels play an important role in the algorithm.peer-reviewe

A Model for Donation Verification

In this paper, we introduce a model for donation verification. A randomized algorithm is developed to check if the money claimed being received by the collector is $(1-\epsilon)$-approximation to the total amount money contributed by the donors. We also derive some negative results that show it is impossible to verify the donations under some circumstances

Bayesian Verification under Model Uncertainty

Machine learning enables systems to build and update domain models based on runtime observations. In this paper, we study statistical model checking and runtime verification for systems with this ability. Two challenges arise: (1) Models built from limited runtime data yield uncertainty to be dealt with. (2) There is no definition of satisfaction w.r.t. uncertain hypotheses. We propose such a definition of subjective satisfaction based on recently introduced satisfaction functions. We also propose the BV algorithm as a Bayesian solution to runtime verification of subjective satisfaction under model uncertainty. BV provides user-definable stochastic bounds for type I and II errors. We discuss empirical results from an example application to illustrate our ideas.Comment: Accepted at SEsCPS @ ICSE 201

Anytime system level verification via parallel random exhaustive hardware in the loop simulation

System level verification of cyber-physical systems has the goal of verifying that the whole (i.e., software + hardware) system meets the given specifications. Model checkers for hybrid systems cannot handle system level verification of actual systems. Thus, Hardware In the Loop Simulation (HILS) is currently the main workhorse for system level verification. By using model checking driven exhaustive HILS, System Level Formal Verification (SLFV) can be effectively carried out for actual systems. We present a parallel random exhaustive HILS based model checker for hybrid systems that, by simulating all operational scenarios exactly once in a uniform random order, is able to provide, at any time during the verification process, an upper bound to the probability that the System Under Verification exhibits an error in a yet-to-be-simulated scenario (Omission Probability). We show effectiveness of the proposed approach by presenting experimental results on SLFV of the Inverted Pendulum on a Cart and the Fuel Control System examples in the Simulink distribution. To the best of our knowledge, no previously published model checker can exhaustively verify hybrid systems of such a size and provide at any time an upper bound to the Omission Probability

The Construction of Verification Models for Embedded Systems

The usefulness of verification hinges on the quality of the verification model. Verification is useful if it increases our confidence that an artefact bahaves as expected. As modelling inherently contains non-formal elements, the qualityof models cannot be captured by purely formal means. Still, we argue that modelling is not an act of irrationalism and unpredictable geniality, but follows rational arguments, that often remain implicit. In this paper we try to identify the tacit rationalism in the model construction as performed by most people doing modelling for verification. By explicating the different phases, arguments, and design decisions in the model construction, we try to develop guidelines that help to improve the process of model construction and the quality of models

A Vision of Collaborative Verification-Driven Engineering of Hybrid Systems

Abstract. Hybrid systems with both discrete and continuous dynamics are an important model for real-world physical systems. The key challenge is how to ensure their correct functioning w.r.t. safety requirements. Promising techniques to ensure safety seem to be model-driven engineering to develop hybrid systems in a well-defined and traceable manner, and formal verification to prove their correctness. Their combination forms the vision of verification-driven engineering. Despite the remarkable progress in automating formal verification of hybrid systems, the construction of proofs of complex systems often requires significant human guidance, since hybrid systems verification tools solve undecidable problems. It is thus not uncommon for verification teams to consist of many players with diverse expertise. This paper introduces a verification-driven engineering toolset that extends our previous work on hybrid and arithmetic verification with tools for (i) modeling hybrid systems, (ii) exchanging and comparing models and proofs, and (iii) managing verification tasks. This toolset makes it easier to tackle large-scale verification tasks.

Extending the Real-Time Maude Semantics of Ptolemy to Hierarchical DE Models

This paper extends our Real-Time Maude formalization of the semantics of flat Ptolemy II discrete-event (DE) models to hierarchical models, including modal models. This is a challenging task that requires combining synchronous fixed-point computations with hierarchical structure. The synthesis of a Real-Time Maude verification model from a Ptolemy II DE model, and the formal verification of the synthesized model in Real-Time Maude, have been integrated into Ptolemy II, enabling a model-engineering process that combines the convenience of Ptolemy II DE modeling and simulation with formal verification in Real-Time Maude.Comment: In Proceedings RTRTS 2010, arXiv:1009.398