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All PMSAT algorithms based on UNSAT core generation are dependent upon two essential external components: (1) a CNF encoder for Boolean cardinality constraints, which expresses constraints in CNF representation; and (2) a SAT solver, which checks the satisfiability state of the SAT instance and extracts UNSAT cores.
Brief overview of the topics addressed in the paper, namely the CNF encoding problem and PMSAT algorithms using UNSAT core generation are given in Section 2.
UNSAT-based methods consist in using iteratively SAT solvers to identify and relax UNSAT formulas in PMSAT instances.
In order to quantify the impact of CNF encoding methods on the performance of UNSAT-based PMSAT solvers, we implement and test a PMSAT solver based on the following CNF encoding methods for AtMost-1 constraint: pairwise, parallel, and sequential encodings [24], In the literature only few competitive SAT solvers generating UNSAT cores are described.