| Autor: |
Kshitij Bansal, Clark Barrett, Andrew Reynolds, Cesare Tinelli |
| Jazyk: |
angličtina |
| Rok vydání: |
2018 |
| Předmět: |
|
| Zdroj: |
Logical Methods in Computer Science, Vol Volume 14, Issue 4 (2018) |
| Druh dokumentu: |
article |
| ISSN: |
1860-5974 |
| DOI: |
10.23638/LMCS-14(4:12)2018 |
| Popis: |
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. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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