Polynomial constraints for sets with cardinality bounds

Authors:
Bruno Marnette;Viktor Kuncak;Martin Rinard
Affiliations:
ENS de Cachan, France;MIT CSAIL, Cambridge;MIT CSAIL, Cambridge
Venue:
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
Year:
2007

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Abstract

Logics that can reason about sets and their cardinality bounds are useful in program analysis, program verification, databases, and knowledge bases. This paper presents a class of constraints on sets and their cardinalities for which the satisfiability and the entailment problems are computable in polynomial time. Our class of constraints, based on tree-shaped formulas, is unique in being simultaneously tractable and able to express 1) that a set is a union of other sets, 2) that sets are disjoint, and 3) that a set has cardinality within a given range. As the main result we present a polynomial-time algorithm for checking entailment of our constraints.