Revisiting Enumerative Instantiation

Andrew Reynolds (1) , Haniel Barbosa (2, 3) , Pascal Fontaine (2, 3)

1 University of Iowa [Iowa City]
2 VERIDIS - Modeling and Verification of Distributed Algorithms and Systems
3 MOSEL - Proof-oriented development of computer-based systems

Formal methods applications often rely on SMT solvers to automatically discharge proof obligations. SMT solvers handle quantified formulas using incomplete heuristic techniques like E-matching, and often resort to model-based quantifier instantiation (MBQI) when these techniques fail. This paper revisits enumerative instantiation, a technique that considers instantiations based on exhaustive enumeration of ground terms. Although simple, we argue that enumer-ative instantiation can supplement other instantiation techniques and be a viable alternative to MBQI for valid proof obligations. We first present a stronger Her-brand Theorem, better suited as a basis for the instantiation loop used in SMT solvers; it furthermore requires considering less instances than classical Herbrand instantiation. Based on this result, we present different strategies for combining enumerative instantiation with other instantiation techniques in an effective way. The experimental evaluation shows that the implementation of these new techniques in the SMT solver CVC4 leads to significant improvements in several benchmark libraries, including many stemming from verification efforts.

Domaines: Logique en informatique [cs.LO]

Andrew Reynolds, Haniel Barbosa, Pascal Fontaine. Revisiting Enumerative Instantiation. TACAS 2018 - 24th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, Apr 2018, Thessaloniki, Greece. pp.20. ⟨hal-01877055⟩