Temporal Logic Verification of Stochastic Systems Using Barrier Certificates

TL;DR

This paper introduces a barrier certificate-based method for efficiently verifying complex temporal properties of stochastic systems without discretization, applicable to high-dimensional cases.

Contribution

It presents a novel, discretization-free approach using barrier certificates for temporal logic verification of stochastic systems, reducing computational complexity.

Findings

Efficient lower bounds on satisfaction probabilities are computed.

Method scales well to high-dimensional systems.

Validated on systems with linear and polynomial dynamics.

Abstract

This paper presents a methodology for temporal logic verification of discrete-time stochastic systems. Our goal is to find a lower bound on the probability that a complex temporal property is satisfied by finite traces of the system. Desired temporal properties of the system are expressed using a fragment of linear temporal logic, called safe LTL over finite traces. We propose to use barrier certificates for computations of such lower bounds, which is computationally much more efficient than the existing discretization-based approaches. The new approach is discretization-free and does not suffer from the curse of dimensionality caused by discretizing state sets. The proposed approach relies on decomposing the negation of the specification into a union of sequential reachabilities and then using barrier certificates to compute upper bounds for these reachability probabilities. We demonstrate the effectiveness of the proposed approach on case studies with linear and polynomial dynamics.