Despite the semantic simplicity of cardinality constraints, the CNF encodings typically used to solve them invariably turn one constraint into a large number of CNF clauses and/or auxiliary variables. This incurs a significant cost, both in space complexity and in runtime, that could be avoided by reasoning about cardinality constraints directly within a solver. Adding a single, native cardi-na...

Maximum Satisfiability (MaxSAT) is an optimization variant of the Boolean Satisfiability (SAT) problem. In general, MaxSAT algorithms perform a succession of SAT solver calls to reach an optimum solution making extensive use of cardinality constraints. Many of these algorithms are non-incremental in nature, i.e. at each iteration the formula is rebuilt and no knowledge is reused from one iterat...

Entity relationship (ER) schemas include cardinality constraints, that restrict the dependencies among entities within a relationship type. The cardinality constraints have direct impact on the application maintenance, since insertions or deletions of entities or relationships might affect related entities. Indeed, maintenance of a system or of a database can be strengthened to enforce consiste...

We introduce pairwise cardinality networks, networks of comparators, derived from pairwise sorting networks, which express cardinality constraints. We show that pairwise cardinality networks are superior to the cardinality networks introduced in previous work which are derived from odd-even sorting networks. Our presentation identifies the precise relationship between odd-even and pairwise sort...

Proving quantitative properties of programs, such as bounds on resource usage or information leakage, often leads to verification conditions that involve cardinalities of sets. Existing approaches for dealing with such verification conditions operate by checking cardinality bounds for given formulas. However, they cannot synthesize formulas that satisfy given cardinality constraints, which limi...