Evaluation of Cardinality Constraints on SMT-Based Debugging

For formal verification of hardware Satisfiability Modulo Theory (SMT) solvers are increasingly applied. Today's state-of-the-art SMT solvers use different techniques like term-rewriting, abstraction, or bit-blasting. The performance does not only depend on the underlying decision problem but also on the encoding of the original problem into an SMT instance. In this work, encodings for cardinality constraints in SMT are investigated. Three different encodings are considered: an adder network, an encoding with multiplexors, and a newly proposed encoding with shifters. The encodings are analyzed with respect to size and complexity. The experimental evaluation on debugging instances that contain cardinality constraints shows the strong influence of the encoding on the resulting run-times.