Clause Size Reduction with all-UIP Learning

Almost all CDCL SAT solvers use the 1-UIP clause learning scheme for learning new clauses from conflicts, and our current understanding of SAT solving provides good reasons for using that scheme. In particular, the 1-UIP scheme yields asserting clauses, and these asserting clauses have minimum LBD among all possible asserting clauses. As a result of these advantages, other clause learning schemes, like i-UIP and all-UIP, that were proposed in early work are not used in modern solvers. In this paper, we propose a new technique for exploiting the all-UIP clause learning scheme. Our technique is to employ all-UIP learning under the constraint that the learnt clause’s LBD does not increase (over the minimum established by the 1-UIP clause). Our method can learn clauses that are significantly smaller than the 1-UIP clause while preserving the minimum LBD. Unlike previous clause minimization methods, our technique is not limited to learning a sub-clause of the 1-UIP clause. We show empirically that our method can improve the performance of state of the art solvers.