Decomposing SAT Instances with Pseudo Backbones

Abstract

Two major search paradigms have been proposed for SAT solving: Systematic Search (SS) and Stochastic Local Search (SLS). In SAT competitions, while SLS solvers are effective on uniform random instances, SS solvers dominate SLS solvers on application instances with internal structures. One important structural property is decomposability. SS solvers have long been exploited the decomposability of application instances with success. We conjecture that SLS solvers can be improved by exploiting decomposability of application instances, and propose the first step toward exploiting decomposability with SLS solvers using pseudo backbones. We then propose two SAT-specific optimizations that lead to better decomposition than on general pseudo Boolean optimization problems. Our empirical study suggests that pseudo backbones can vastly simplify SAT instances, which further results in decomposing the instances into thousands of connected components. This decomposition serves as a key stepping stone for applying the powerful recombination operator, partition crossover, to the SAT domain. Moreover, we establish a priori analysis for identifying problem instances with potential decomposability using visualization of MAXSAT instances and treewidth.