# Quantifier Instantiation Techniques for Finite Model Finding in SMT

Quantifier Instantiation Techniques for Finite Model Finding in SMT” by Andrew Reynolds, Cesare Tinelli, Amit Goel, Sava Krstic, Morgan Deters, and Clark Barrett. In Proceedings of the 24^th International Conference on Automated Deduction (CADE '13), (Maria Paola Bonacina, ed.), 2013, pp. 377-391. Lake Placid, NY.

## Abstract

SMT-based applications increasingly rely on SMT solvers being able to deal with quantified formulas. Current work shows that for formulas with quantifiers over uninterpreted sorts counter-models can be obtained by integrating a finite model finding capability into the architecture of a modern SMT solver. We examine various strategies for on-demand quantifier instantiation in this setting. Here, completeness can be achieved by considering all ground instances over the finite domain of each quantifier. However, exhaustive instantiation quickly becomes unfeasible with larger domain sizes. We propose instantiation strategies to identify and consider only a selection of ground instances that suffices to determine the satisfiability of the input formula. We also examine heuristic quantifier instantiation techniques such as E-matching for the purpose of accelerating the search. We give experimental evidence that our approach is practical for use in industrial applications and is competitive with other approaches.

BibTeX entry:

@inproceedings{RTG+13,
author = {Andrew Reynolds and Cesare Tinelli and Amit Goel and Sava
Krstic and Morgan Deters and Clark Barrett},
editor = {Maria Paola Bonacina},
title = {Quantifier Instantiation Techniques for Finite Model Finding
in {SMT}},
booktitle = {Proceedings of the {\it 24^{th}} International Conference