StocHy: automated verification and synthesis of stochastic processes

StocHy is a software tool for the quantitative analysis of discrete-time stochastic hybrid systems (SHS). StocHy accepts a high-level description of stochastic models and constructs an equivalent SHS model. The tool allows to (i) simulate the SHS evolution over a given time horizon; and to automatically construct formal abstractions of the SHS. Abstractions are then employed for (ii) formal verification or (iii) control (policy, strategy) synthesis. StocHy allows for modular modelling, and has separate simulation, verification and synthesis engines, which are implemented as independent libraries. This allows for libraries to be easily used and for extensions to be easily built. The tool is implemented in C++ and employs manipulations based on vector calculus, the use of sparse matrices, the symbolic construction of probabilistic kernels, and multi-threading. Experiments show StocHy's markedly improved performance when compared to existing abstraction-based approaches: in particular, StocHy beats state-of-the-art tools in terms of precision (abstraction error) and computational effort, and finally attains scalability to large-sized models (12 continuous dimensions). StocHy is available at www.gitlab.com/natchi92/StocHy

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

Bounded Verification with On-the-Fly Discrepancy Computation

Simulation-based verification algorithms can provide formal safety guarantees for nonlinear and hybrid systems. The previous algorithms rely on user provided model annotations called discrepancy function, which are crucial for computing reachtubes from simulations. In this paper, we eliminate this requirement by presenting an algorithm for computing piece-wise exponential discrepancy functions. The algorithm relies on computing local convergence or divergence rates of trajectories along a simulation using a coarse over-approximation of the reach set and bounding the maximal eigenvalue of the Jacobian over this over-approximation. The resulting discrepancy function preserves the soundness and the relative completeness of the verification algorithm. We also provide a coordinate transformation method to improve the local estimates for the convergence or divergence rates in practical examples. We extend the method to get the input-to-state discrepancy of nonlinear dynamical systems which can be used for compositional analysis. Our experiments show that the approach is effective in terms of running time for several benchmark problems, scales reasonably to larger dimensional systems, and compares favorably with respect to available tools for nonlinear models.Comment: 24 page

On-Line Monitoring for Temporal Logic Robustness

In this paper, we provide a Dynamic Programming algorithm for on-line monitoring of the state robustness of Metric Temporal Logic specifications with past time operators. We compute the robustness of MTL with unbounded past and bounded future temporal operators MTL over sampled traces of Cyber-Physical Systems. We implemented our tool in Matlab as a Simulink block that can be used in any Simulink model. We experimentally demonstrate that the overhead of the MTL robustness monitoring is acceptable for certain classes of practical specifications

Proving Abstractions of Dynamical Systems through Numerical Simulations

A key question that arises in rigorous analysis of cyberphysical systems under attack involves establishing whether or not the attacked system deviates significantly from the ideal allowed behavior. This is the problem of deciding whether or not the ideal system is an abstraction of the attacked system. A quantitative variation of this question can capture how much the attacked system deviates from the ideal. Thus, algorithms for deciding abstraction relations can help measure the effect of attacks on cyberphysical systems and to develop attack detection strategies. In this paper, we present a decision procedure for proving that one nonlinear dynamical system is a quantitative abstraction of another. Directly computing the reach sets of these nonlinear systems are undecidable in general and reach set over-approximations do not give a direct way for proving abstraction. Our procedure uses (possibly inaccurate) numerical simulations and a model annotation to compute tight approximations of the observable behaviors of the system and then uses these approximations to decide on abstraction. We show that the procedure is sound and that it is guaranteed to terminate under reasonable robustness assumptions