Model Checking modulo Strong Proof Systems

Objective

Ensuring that computerized systems adhere to their specifications is of paramount importance to our everyday life. Model Checking (MC) is an automatic formal verification technique for establishing a system’s correctness. Given a model and a specification, it can construct a proof of whether the specification is valid in that model or not. Proof systems provide formal proof for the validity of a statement under a given set of axioms and are a powerful tool when applying logic in automated reasoning. MC can be viewed as a proof-search algorithm that operates in some proof system. While MC is widely used in the industry to rigorously establish correctness of computerized systems, its application remains a challenge due to the complexity of implementing efficient proof-search algorithms that construct proofs automatically. The goal of StrongMC is to develop the theory and algorithms to enable the use of strong proof systems, which admit short proofs, in model checking. There is an inherent trade-off between the strength of a proof system and the ability to implement an efficient proof-search algorithm for it. As the strength of the proof system increases, so does the size of the search space, making proof-search algorithms intractable and hence our goal is ambitious and challenging. Yet, based on our preliminary results, we conjecture that strong proof systems can be used efficiently in model checking. By probing three thrusts, we aim to tackle this challenge: (1) use decision procedures that utilize strong proof systems in MC; (2) develop MC algorithms that are based on the Extended Resolution proof system; (3) Analyzing the complexity and efficiency of MC algorithms that use strong proof systems from both theoretical and practical points of view. We expect the new theoretical foundation and the enhanced MC algorithms will lead to the widespread practical adoption of MC, while also having an important impact on many related fields in Formal Methods.