Detecting Cardinality Constraints in CNF

We present novel approaches to detect cardinality constraints expressed in CNF. The first approach is based on a syntactic analysis of specific data structures used in SAT solvers to represent binary and ternary clauses, whereas the second approach is based on a semantic analysis by unit propagation. The syntactic approach computes an approximation of the cardinality constraints AtMost-1 and AtMost-2 constraints very fast, whereas the semantic approach has the property to be generic, i.e. it can detect cardinality constraints AtMost-k for any k, at a higher computation cost. Our experimental results suggest that both approaches are efficient at recovering AtMost-1 and AtMost-2 cardinality constraints.