Constraint solving for finite model finding in SMT solvers

Abstract

SMT solvers have been used successfully as reasoning engines for automated verification and other applications based on automated reasoning. Current techniques for dealing with quantified formulas in SMT are generally incomplete, forcing SMT solvers to report "unknown" when they fail to prove the unsatisfiability of a formula with quantifiers. This inability to return counter-models limits their usefulness in applications that produce queries involving quantified formulas. In this paper, we reduce these limitations by integrating finite model finding techniques based on constraint solving into the architecture used by modern SMT solvers. This approach is made possible by a novel solver for cardinality constraints, as well as techniques for on-demand instantiation of quantified formulas. Experiments show that our approach is competitive with the state of the art in SMT, and orthogonal to approaches in automated theorem proving.

Explorations in static pointer analysis

“…Finally, a closely related notion is that of satisfiability modulo theories solvers [85,126] (or abbreviated as SMT solvers). Satisfiability modulo theories generalizes Boolean satisfiability (SAT) by adding a combinations of background theories such as: equality reasoning, arithmetic, fixed-size bit-vectors, arrays, uninterpreted functions, and other useful firstorder theories.…”