Syntax-Guided Quantifier Instantiation

Abstract

This paper presents a novel approach for quantifier instantiation in Satisfiability Modulo Theories (SMT) that leverages syntax-guided synthesis (SyGuS) to choose instantiation terms. It targets quantified constraints over background theories such as (non)linear integer, reals and floating-point arithmetic, bit-vectors, and their combinations. Unlike previous approaches for quantifier instantiation in these domains which rely on theory-specific strategies, the new approach can be applied to any (combined) theory, when provided with a grammar for instantiation terms for all sorts in the theory. We implement syntax-guided instantiation in the SMT solver CVC4, leveraging its support for enumerative SyGuS. Our experiments demonstrate the versatility of the approach, showing that it is competitive with or exceeds the performance of state-of-the-art solvers on a range of background theories.