# Quantifier Instantiation Techniques for Finite Model Finding in SMT

@inproceedings{Reynolds2013QuantifierIT, title={Quantifier Instantiation Techniques for Finite Model Finding in SMT}, author={Andrew Reynolds and Cesare Tinelli and Amit Goel and Sava Krstic and Morgan Deters and Clark W. Barrett}, booktitle={CADE}, year={2013} }

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… Expand

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#### 68 Citations

Finite Model Finding in SMT

- Computer Science
- CAV
- 2013

A novel finite model finding method that reduces limitations in the case of quantifiers ranging over free sorts in SMT by not relying on the introduction of domain constants for the free sorts and by being fully integrated into the general architecture used by most SMT solvers. Expand

Conflicts, Models and Heuristics for Quantifier Instantiation in SMT

- Computer Science
- Vampire@IJCAR
- 2016

An overview of recent advances in quantifier instantiation in SMT is given, including the well-known technique known as E-matching, and new instantiation-based techniques that are specialized to background theories such as linear real and integer arithmetic are mentioned. Expand

SMT formula Model UNSAT SMT solver Instantiation module

- 2018

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… Expand

Constraint solving for finite model finding in SMT solvers*

- Computer Science, Mathematics
- Theory and Practice of Logic Programming
- 2017

This paper integrates finite model finding techniques based on constraint solving into the architecture used by modern SMT solvers, made possible by a novel solver for cardinality constraints, as well as techniques for on-demand instantiation of quantified formulas. Expand

Revisiting Enumerative Instantiation

- Computer Science
- TACAS
- 2018

This paper revisits enumerative instantiation, a technique that considers instantiations based on exhaustive enumeration of ground terms, and presents a stronger Herbrand Theorem, better suited as a basis for the instantiation loop used in SMT solvers. Expand

Syntax-Guided Quantifier Instantiation

- Computer Science
- TACAS
- 2021

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… Expand

On Counterexample Guided Quantifier Instantiation for Synthesis in CVC4

- Computer Science, Mathematics
- ArXiv
- 2015

We introduce the first program synthesis engine implemented inside an SMT solver. We present an approach that extracts solution functions from unsatisfiability proofs of the negated form of synthesis… Expand

Counterexample-Guided Quantifier Instantiation for Synthesis in SMT

- Computer Science
- CAV
- 2015

We introduce the first program synthesis engine implemented inside an SMT solver. We present an approach that extracts solution functions from unsatisfiability proofs of the negated form of synthesis… Expand

On Satisfiability for Quantified Formulas in Instantiation-Based Procedures

- Mathematics
- 2016

Procedures for first-order logic with equality are used in many modern theorem provers and solvers, yet procedure termination in case of interesting sub-classes of satisfiable formulas remains a… Expand

Extending SMT Solvers to Higher-Order Logic

- Computer Science
- CADE
- 2019

This work proposes a pragmatic extension for SMT solvers to support HOL reasoning natively without compromising performance on FOL reasoning, thus leveraging the extensive research and implementation efforts dedicated to efficient SMT solving. Expand

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