Quantitative Safety: Linking Proof-Based Verification with Model Checking for Probabilistic Systems

TL;DR

This paper introduces a method that combines proof-based verification with model checking to evaluate probabilistic safety properties, implemented in a prototype system called YAGA for transforming proof models into verifiable probabilistic models.

Contribution

It presents a new theorem, a verification procedure, and a prototype system that bridges proof-based and model checking approaches for probabilistic systems.

Findings

Successful transformation of proof models into PRISM models with reward structures

Verification of probabilistic safety properties using the prototype system

Application demonstrated on a probabilistic library case study

Abstract

This paper presents a novel approach for augmenting proof-based verification with performance-style analysis of the kind employed in state-of-the-art model checking tools for probabilistic systems. Quantitative safety properties usually specified as probabilistic system invariants and modeled in proof-based environments are evaluated using bounded model checking techniques. Our specific contributions include the statement of a theorem that is central to model checking safety properties of proof-based systems, the establishment of a procedure; and its full implementation in a prototype system (YAGA) which readily transforms a probabilistic model specified in a proof-based environment to its equivalent verifiable PRISM model equipped with reward structures. The reward structures capture the exact interpretation of the probabilistic invariants and can reveal succinct information about the model during experimental investigations. Finally, we demonstrate the novelty of the technique on a probabilistic library case study.