## Bansal, Kshitij and Barrett, Clark and Reynolds, Andrew and Tinelli, Cesare - Reasoning with Finite Sets and Cardinality Constraints in SMT

lmcs:3155 - Logical Methods in Computer Science, November 1, 2018, Volume 14, Issue 4
Reasoning with Finite Sets and Cardinality Constraints in SMT

Authors: Bansal, Kshitij and Barrett, Clark and Reynolds, Andrew and Tinelli, Cesare

We consider the problem of deciding the satisfiability of quantifier-free formulas in the theory of finite sets with cardinality constraints. Sets are a common high-level data structure used in programming; thus, such a theory is useful for modeling program constructs directly. More importantly, sets are a basic construct of mathematics and thus natural to use when formalizing the properties of computational systems. We develop a calculus describing a modular combination of a procedure for reasoning about membership constraints with a procedure for reasoning about cardinality constraints. Cardinality reasoning involves tracking how different sets overlap. For efficiency, we avoid considering Venn regions directly, as done in previous work. Instead, we develop a novel technique wherein potentially overlapping regions are considered incrementally as needed, using a graph to track the interaction among the different regions. The calculus has been designed to facilitate its implementation within SMT solvers based on the DPLL($T$) architecture. Our experimental results demonstrate that the new techniques are competitive with previous techniques and can scale much better on certain classes of problems.

Source : oai:arXiv.org:1702.06259
DOI : 10.23638/LMCS-14(4:12)2018
Volume: Volume 14, Issue 4
Published on: November 1, 2018
Submitted on: February 22, 2017
Keywords: Computer Science - Logic in Computer Science