Heuristically Matching Solution Spaces of Arithmetic Formulas to Efficiently Reuse Solutions

Many symbolic program analysis techniques rely on SMT solvers to verify properties of programs. Despite the remarkable progress made in the development of such tools, SMT solvers still represent a main bottleneck to the scalability of these techniques. Recent approaches tackle this bottleneck by reusing solutions of formulas that recur during program analysis, thus reducing the number of queries to SMT solvers. Current approaches only reuse solutions across formulas that are equivalent to, contained in or implied by other formulas, as identified through a set of predefined rules, and cannot reuse solutions across formulas that differ in their structure, even if they share some potentially reusable solutions. In this paper, we propose a novel approach that can reuse solutions across formulas that share at least one solution, regardless of their structural resemblance. Our approach exploits a novel heuristic to efficiently identify solutions computed for previously solved formulas and most likely shared by new formulas. The results of an empirical evaluation of our approach on two different logics show that our approach can identify on average more reuse opportunities and is markedly faster than competing approaches.