Logo image
Back
Solving Set Constraints with Comprehensions and Bounded Quantifiers
Preprint   Open access

Solving Set Constraints with Comprehensions and Bounded Quantifiers

Mudathir Mohamed, Nick Feng, Andrew Reynolds, Cesare Tinelli, Clark Barrett and Marsha Chechik
ArXiv.org
Cornell University
08/11/2025
DOI: 10.48550/arxiv.2508.08496
url
https://doi.org/10.48550/arxiv.2508.08496View
Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

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.
 Computer Science - Logic in Computer Science

Details

Metrics

33 Record Views
Logo image