Fedor Shmarov

Fedor Shmarov, Paolo Zuliani

We present ProbReach, a tool for verifying probabilistic reachability for stochastic hybrid systems, i.e., computing the probability that the system reaches an unsafe region of the state space. In particular, ProbReach will compute an arbitrarily small interval which is guaranteed to contain the required probability. Standard (non-probabilistic) reachability is undecidable even for linear hybrid systems. In ProbReach we adopt the weaker notion of delta-reachability, in which the unsafe region is overapproximated by a user-defined parameter (delta). This choice leads to false alarms, but also makes the reachability problem decidable for virtually any hybrid system. In ProbReach we have implemented a probabilistic version of delta-reachability that is suited for hybrid systems whose stochastic behaviour is given in terms of random initial conditions. In this paper we introduce the capabilities of ProbReach, give an overview of the parallel implementation, and present results for several benchmarks involving highly non-linear hybrid systems.

Edoardo Manino, Rafael Sá Menezes, Fedor Shmarov et al.

Safety-critical systems with neural network components require strong guarantees. While existing neural network verification techniques have shown great progress towards this goal, they cannot prove the absence of software faults in the network implementation. This paper presents NeuroCodeBench - a verification benchmark for neural network code written in plain C. It contains 32 neural networks with 607 safety properties divided into 6 categories: maths library, activation functions, error-correcting networks, transfer function approximation, probability density estimation and reinforcement learning. Our preliminary evaluation shows that state-of-the-art software verifiers struggle to provide correct verdicts, due to their incomplete support of the standard C mathematical library and the complexity of larger neural networks.

Edoardo Manino, Bruno Farias, Rafael Sá Menezes et al.

The behaviour of neural network components must be proven correct before deployment in safety-critical systems. Unfortunately, existing neural network verification techniques cannot certify the absence of faults at the software level. In this paper, we show how to specify and verify that neural networks are safe, by explicitly reasoning about their floating-point implementation. In doing so, we construct NeuroCodeBench 2.0, a benchmark comprising 912 neural network verification examples that cover activation functions, common layers, and full neural networks of up to 170K parameters. Our verification suite is written in plain C and is compatible with the format of the International Competition on Software Verification (SV-COMP). Thanks to it, we can conduct the first rigorous evaluation of eight state-of-the-art software verifiers on neural network code. The results show that existing automated verification tools can correctly solve an average of 11% of our benchmark, while producing around 3% incorrect verdicts. At the same time, a historical analysis reveals that the release of our benchmark has already had a significantly positive impact on the latter.

Fedor Shmarov, Nicola Paoletti, Ezio Bartocci et al.

We present a new method for the automated synthesis of safe and robust Proportional-Integral-Derivative (PID) controllers for stochastic hybrid systems. Despite their widespread use in industry, no automated method currently exists for deriving a PID controller (or any other type of controller, for that matter) with safety and performance guarantees for such a general class of systems. In particular, we consider hybrid systems with nonlinear dynamics (Lipschitz-continuous ordinary differential equations) and random parameters, and we synthesize PID controllers such that the resulting closed-loop systems satisfy safety and performance constraints given as probabilistic bounded reachability properties. Our technique leverages SMT solvers over the reals and nonlinear differential equations to provide formal guarantees that the synthesized controllers satisfy such properties. These controllers are also robust by design since they minimize the probability of reaching an unsafe state in the presence of random disturbances. We apply our approach to the problem of insulin regulation for type 1 diabetes, synthesizing controllers with robust responses to large random meal disturbances, thereby enabling them to maintain blood glucose levels within healthy, safe ranges.