Certificates and Witnesses for Multi-Objective Queries in Markov Decision Processes

TL;DR

This paper develops certifying algorithms for multi-objective properties in Markov decision processes, providing checkable certificates and witnesses to enhance trust and debugging capabilities in verification.

Contribution

It generalizes certificates and witnesses to multi-objective queries in MDPs using linear programming techniques, including implementation and experimental validation.

Findings

Certificates and witnesses improve verification trustworthiness.

Algorithms successfully handle multi-objective properties.

Experimental results demonstrate practical effectiveness.

Abstract

Certifying verification algorithms not only return whether a given property holds or not, but also provide an accompanying independently checkable certificate and a corresponding witness. The certificate can be used to easily validate the correctness of the result and the witness provides useful diagnostic information, e.g. for debugging purposes. Thus, certificates and witnesses substantially increase the trustworthiness and understandability of the verification process. In this work, we consider certificates and witnesses for multi-objective reachability-invariant and mean-payoff queries in Markov decision processes, that is conjunctions or disjunctions either of reachability and invariant or mean-payoff predicates, both universally and existentially quantified. Thereby, we generalize previous works on certificates and witnesses for single reachability and invariant constraints. To this end, we turn known linear programming techniques into certifying algorithms and show that witnesses in the form of schedulers and subsystems can be obtained. As a proof-of-concept, we report on implementations of certifying verification algorithms and experimental results.