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

中文翻译：

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形式化基于 SAT 的模型检查编码方法的合理性

一种有效的模型检查方法是利用 SAT（或 SMT）求解器的高效决策程序。在基于 SAT 的模型检查中，系统及其属性被编码为一组逻辑公式，并根据公式的可满足性检查安全性。随着编码方法的改进和制作（例如，k-induction 和 IC3/PDR），验证它们的正确性变得更加重要。本研究旨在使用 Coq 证明助手对 SMC 方法进行形式验证。我们的贡献是双重的：（1）我们将 Coq 中的基本编码方法、k-induction 和（简化版本的）IC3/PDR 指定为一组简单的模块化编码谓词。(2) 我们基于我们在状态序列和路径上的形式化引理，提供了编码方法健全性的形式证明。