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arXiv · 2403.07821

Augmenting Interpolation-Based Model Checking with Auxiliary Invariants (Extended Version)

Dirk Beyer·Po-Chun Chien·Nian-Ze Lee
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Abstract

Software model checking is a challenging problem, and generating relevant invariants is a key factor in proving the safety properties of a program. Program invariants can be obtained by various approaches, including lightweight procedures based on data-flow analysis and intensive techniques using Craig interpolation. Although data-flow analysis runs efficiently, it often produces invariants that are too weak to prove the properties. By contrast, interpolation-based approaches build strong invariants from interpolants, but they might not scale well due to expensive interpolation procedures. Invariants can also be injected into model-checking algorithms to assist the analysis. Invariant injection has been studied for many well-known approaches, including k-induction, predicate abstraction, and symbolic execution. We propose an augmented interpolation-based verification algorithm that injects external invariants into interpolation-based model checking (McMillan, 2003), a hardware model-checking algorithm recently adopted for software verification. The auxiliary invariants help prune unreachable states in Craig interpolants and confine the analysis to the reachable parts of a program. We implemented the proposed technique in the verification framework CPAchecker and evaluated it against mature SMT-based methods in CPAchecker as well as other state-of-the-art software verifiers. We found that injecting invariants reduces the number of interpolation queries needed to prove safety properties and improves the run-time efficiency. Consequently, the proposed invariant-injection approach verified difficult tasks that none of its plain version (i.e., without invariants), the invariant generator, or any compared tools could solve.

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Dirk Beyer, Po-Chun Chien, Nian-Ze Lee. 2024-10-25. Augmenting Interpolation-Based Model Checking with Auxiliary Invariants (Extended Version). https://arxiv.org/abs/2403.07821

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