Instantiation of SMT problems modulo Integers

TL;DR

This paper introduces a new, generic, and efficient instantiation technique for SMT problems combining linear arithmetic with other theories, improving decision procedure effectiveness.

Contribution

It proposes a complete instantiation scheme that first handles arithmetic and then eliminates remaining variables using a theory-specific strategy.

Findings

Technique is applicable to a wide range of theories.

Method demonstrates efficiency surpassing existing schemes.

Provides examples showing the method's completeness and practicality.

Abstract

Many decision procedures for SMT problems rely more or less implicitly on an instantiation of the axioms of the theories under consideration, and differ by making use of the additional properties of each theory, in order to increase efficiency. We present a new technique for devising complete instantiation schemes on SMT problems over a combination of linear arithmetic with another theory T. The method consists in first instantiating the arithmetic part of the formula, and then getting rid of the remaining variables in the problem by using an instantiation strategy which is complete for T. We provide examples evidencing that not only is this technique generic (in the sense that it applies to a wide range of theories) but it is also efficient, even compared to state-of-the-art instantiation schemes for specific theories.