ProbReach: Verified Probabilistic Delta-Reachability for Stochastic Hybrid Systems

TL;DR

ProbReach is a tool that verifies probabilistic reachability in stochastic hybrid systems by computing guaranteed probability intervals, making the problem decidable through delta-reachability, and demonstrating effectiveness on complex benchmarks.

Contribution

This paper introduces ProbReach, a novel tool that combines probabilistic delta-reachability with parallel computation for stochastic hybrid systems.

Findings

Successfully verified probabilistic reachability on complex hybrid systems.

Demonstrated the tool's scalability with parallel implementation.

Achieved precise probability bounds despite system non-linearity.

Abstract

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.