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One of the effective model checking methods is to utilize the efficientdecision procedure of SAT (or SMT) solvers. In a SAT-based model checking, asystem and its property are encoded into a set of logic formulas and the safetyis checked based on the satisfiability of the formulas. As the encoding methodsare improved and crafted (e.g., k-induction and IC3/PDR), verifying theircorrectness becomes more important. This research aims at a formal verificationof the SMC methods using the Coq proof assistant. Our contributions aretwofold: (1) We specify the basic encoding methods, k-induction and (asimplified version of) IC3/PDR in Coq as a set of simple and modular encodingpredicates. (2) We provide a formal proof of the soundness of the encodingmethods based on our formalized lemmas on state sequences and paths.

Formalizing the Soundness of the Encoding Methods of SAT-based Model Checking