Combining bounded solving and controllable randomization for approximate model counting

Abstract

ABSTRACT Propositional model counting is the problem of computing the satisfying assignments count of a given CNF formula. Due to the weak solving ability of the existing exact model counters in large-scale problems, approximate model counting has been proposed as a practical alternative to exact model counting. Most of the best current approaches are based on XOR constraints for approximate model counting, also known as the hashing-based method. In this paper, a new approximate model counter using short XOR constraints is proposed, which integrates bounded solving and controllable randomisation. By constantly adding short XOR constants, the solution space has been reduced to a smaller one. However, a smaller scale of solution space may result in worse result accuracy. Therefore, by limiting the scale of solution space that applies XOR constraints, bounded solving effectively increases the accuracy of a model counter. Controllable randomisation makes use of backbone variables and the constraint level among variables, such that the short XOR constraints can reach the same reduction effect on solution space as the long ones. It improves the quality of XOR constraints as well as the SAT solving efficiency. Experimentally, we demonstrate that in almost every benchmark used in well-known ApproxMC2 and STAC_CNF, our approach outperforms the existing approximate model counters in both accuracy and efficiency.