Solving Set Constraints with Comprehensions and Bounded Quantifiers

TL;DR

This paper introduces a novel approach using set-bounded quantifiers and a filter operator to improve SMT solving of quantified formulas, outperforming existing techniques on certain benchmarks.

Contribution

The paper presents a new method leveraging set-bounded quantifiers and a filter operator, demonstrating improved performance over existing SMT solving techniques for quantified formulas.

Findings

Outperforms other quantification techniques on satisfiable problems.

Competitive results on unsatisfiable benchmarks compared to LEGOS.

Identifies a decidable class of constraints with restricted filter applications.

Abstract

Many real applications problems can be encoded easily as quantified formulas in SMT. However, this simplicity comes at the cost of difficulty during solving by SMT solvers. Different strategies and quantifier instantiation techniques have been developed to tackle this. However, SMT solvers still struggle with quantified formulas generated by some applications. In this paper, we discuss the use of set-bounded quantifiers, quantifiers whose variable ranges over a finite set. These quantifiers can be implemented using quantifier-free fragment of the theory of finite relations with a filter operator, a form of restricted comprehension, that constructs a subset from a finite set using a predicate. We show that this approach outperforms other quantification techniques in satisfiable problems generated by the SLEEC tool, and is very competitive on unsatisfiable benchmarks compared to LEGOS, a specialized solver for SLEEC. We also identify a decidable class of constraints with restricted applications of the filter operator, while showing that unrestricted applications lead to undecidability.