Revisiting Assumptions Ordering in CAR-Based Model Checking

TL;DR

This paper investigates the impact of assumption ordering in CAR-based model checking, proposing improved strategies that enhance performance and outperform existing algorithms in bug detection.

Contribution

It introduces a new assumption ordering strategy based on locality of cores and a hybrid approach that dynamically switches strategies during verification.

Findings

Hybrid-CAR outperforms fixed strategies and state-of-the-art bug-finding algorithms.

Locality of cores explains the effectiveness of assumption ordering strategies.

Empirical evaluation demonstrates significant performance improvements.

Abstract

Model checking is an automatic formal verification technique that is widely used in hardware verification. The state-of-the-art complete model-checking techniques, based on IC3/PDR and its general variant CAR, are based on computing symbolically sets of under - and over-approximating state sets (called frames) with multiple calls to a SAT solver. The performance of those techniques is sensitive to the order of the assumptions with which the SAT solver is invoked, because it affects the unsatisfiable cores - which the solver emits when the formula is unsatisfiable - that crucially affect the search process. This observation was previously published in [15], where two partial assumption ordering strategies, intersection and rotation were suggested (partial in the sense that they determine the order of only a subset of the literals). In this paper we extend and improve these strategies based on an analysis of the reason for their effectiveness. We prove that intersection is effective because of what we call locality of the cores, and our improved strategy is based on this observation. We conclude our paper with an extensive empirical evaluation of the various ordering techniques. One of our strategies, Hybrid-CAR, which switches between strategies at runtime, not only outperforms other, fixed ordering strategies, but also outperforms other state-of-the-art bug-finding algorithms such as ABC-BMC.