Refinement and Difference for Probabilistic Automata

TL;DR

This paper introduces an algorithm to approximate the difference between two Abstract Probabilistic Automata with arbitrary precision, aiding the analysis of stochastic system specifications.

Contribution

It presents a novel algorithm leveraging new distance measures between APAs to approximate differences, enhancing refinement analysis capabilities.

Findings

The algorithm achieves arbitrary approximation precision.

It relies on new quantitative distance notions.

The method is as effective and straightforward as refinement checking.

Abstract

This paper studies a difference operator for stochastic systems whose specifications are represented by Abstract Probabilistic Automata (APAs). In the case refinement fails between two specifications, the target of this operator is to produce a specification APA that represents all witness PAs of this failure. Our contribution is an algorithm that allows to approximate the difference of two APAs with arbitrary precision. Our technique relies on new quantitative notions of distances between APAs used to assess convergence of the approximations, as well as on an in-depth inspection of the refinement relation for APAs. The procedure is effective and not more complex to implement than refinement checking.