Global Guidance for Local Generalization in Model Checking

Abstract

SMT-based model checkers, especially IC3-style ones, are currently the most effective techniques for verification of infinite state systems. They infer global inductive invariants via local reasoning about a single step of the transition relation of a system, while employing SMTbased procedures, such as interpolation, to mitigate the limitations of local reasoning and allow for better generalization. Unfortunately, these mitigations intertwine model checking with heuristics of the underlying SMT-solver, negatively affecting stability of model checking. In this paper, we propose to tackle the limitations of locality in a systematic manner. We introduce explicit global guidance into the local reasoning performed by IC3-style algorithms. To this end, we extend the SMT-IC3 paradigm with three novel rules, designed to mitigate fundamental sources of failure that stem from locality. We instantiate these rules for the theory of Linear Integer Arithmetic and implement them on top of Spacer solver in Z3. Our empirical results show that GSpacer, Spacer extended with global guidance, is significantly more effective than both Spacer and sole global reasoning, and, furthermore, is insensitive to interpolation.

Program Verification with Constrained Horn Clauses (Invited Paper)

“…Extension for quantified solutions, which are necessary for establishing interesting properties when arrays are involved is described in [20]. More recently, the interpolation for lemma-generalization has been replaced by more global guidance [14]. This made Spacer competitive with other data-driven approaches that infer new lemmas based on numerical values of blocked counterexamples.…”

Competition Report: CHC-COMP-21

“…These include interpolation, inductive generalization and quantifier generalization. The latest version of Spacer presents a new heuristic for learning lemmas [10,11].…”

Word level property directed reachability

“…Global Guidance for Spacer. [24] introduced three global guidance rules for Spacer. These rules were designed to allow Spacer to detect and correct itself when it diverges.…”

“…However, there are no interpolation strategies for BV, that would be always effective. Therefore, we instantiate the global guidance rules recently proposed in [24] and obtain an effective alternative to interpolation.…”