SReach: A Bounded Model Checker for Stochastic Hybrid Systems

TL;DR

SReach is a novel tool that combines randomized sampling, $elta$-complete decision procedures, and statistical tests to solve probabilistic reachability problems in nonlinear and stochastic hybrid systems, providing soundness and improved coverage.

Contribution

It introduces a new approach that encodes stochastic information with random variables and integrates multiple techniques to effectively analyze complex hybrid systems.

Findings

Successfully applied to biological models and benchmarks

Supports non-deterministic branching and improves simulation coverage

Provides sound probabilistic reachability analysis with small error bounds

Abstract

In this paper we describe a new tool, SReach, which solves probabilistic bounded reachability problems for two classes of stochastic hybrid systems. The first one is (nonlinear) hybrid automata with parametric uncertainty. The second one is probabilistic hybrid automata with additional randomness for both transition probabilities and variable resets. Standard approaches to reachability problems for linear hybrid systems require numerical solutions for large optimization problems, and become infeasible for systems involving both nonlinear dynamics over the reals and stochasticity. Our approach encodes stochastic information by using random variables, and combines the randomized sampling, a $\delta$-complete decision procedure, and statistical tests. SReach utilizes the $\delta$-complete decision procedure to solve reachability problems in a sound manner, i.e., it always decides correctly if, for a given assignment to all random variables, the system actually reaches the unsafe region. The statistical tests adapted guarantee arbitrary small error bounds between probabilities estimated by SReach and real ones. Compared to standard simulation-based methods, our approach supports non-deterministic branching, increases the coverage of simulation, and avoids the zero-crossing problem. We demonstrate our method's feasibility by applying SReach to three representative biological models and to additional benchmarks for nonlinear hybrid systems with multiple probabilistic system parameters.