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

lmcs:3155 - Logical Methods in Computer Science, November 1, 2018, Volume 14, Issue 4 - https://doi.org/10.23638/LMCS-14(4:12)2018
Reasoning with Finite Sets and Cardinality Constraints in SMT

Authors: Kshitij Bansal ; Clark Barrett ; Andrew Reynolds ; Cesare Tinelli

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.

Volume: Volume 14, Issue 4
Published on: November 1, 2018
Accepted on: November 1, 2018
Submitted on: February 22, 2017
Keywords: Computer Science - Logic in Computer Science
Fundings :
Source : OpenAIRE Research Graph
• TWC: Medium: Collaborative: Breaking the Satisfiability Modulo Theories (SMT) Bottleneck in Symbolic Security Analysis; Funder: National Science Foundation; Code: 1228768
• TWC: Medium: Collaborative: Breaking the Satisfiability Modulo Theories (SMT) Bottleneck in Symbolic Security Analysis; Funder: National Science Foundation; Code: 1228765
• SHF: Small: Integrating separation logic and SMT for better heap verification; Funder: National Science Foundation; Code: 1320583