Formalization of Abstract State Transition Systems for SAT

TL;DR

This paper formalizes modern SAT solvers as abstract state transition systems within Isabelle/HOL, proving their correctness and covering a range of solver procedures, including DPLL and its successors.

Contribution

It provides a machine-verifiable formalization of SAT solvers' transition systems, with general specifications and weaker assumptions for correctness proofs.

Findings

Formalization covers classical and modern SAT solvers.

Proves total correctness: soundness, termination, completeness.

Provides machine-verifiable correctness proofs in Isabelle/HOL.

Abstract

We present a formalization of modern SAT solvers and their properties in a form of abstract state transition systems. SAT solving procedures are described as transition relations over states that represent the values of the solver's global variables. Several different SAT solvers are formalized, including both the classical DPLL procedure and its state-of-the-art successors. The formalization is made within the Isabelle/HOL system and the total correctness (soundness, termination, completeness) is shown for each presented system (with respect to a simple notion of satisfiability that can be manually checked). The systems are defined in a general way and cover procedures used in a wide range of modern SAT solvers. Our formalization builds up on the previous work on state transition systems for SAT, but it gives machine-verifiable proofs, somewhat more general specifications, and weaker assumptions that ensure the key correctness properties. The presented proofs of formal correctness of the transition systems can be used as a key building block in proving correctness of SAT solvers by using other verification approaches.