Boolean Rings for Intersection-Based Satisfiability

A potential advantage of using a Boolean-ring formalism for propositional formulæ is the large measure of simplification it facilitates. We propose a combined linear and binomial representation for Boolean-ring polynomials with which one can easily apply Gaussian elimination and Horn-clause methods to advantage. We demonstrate that this framework, with its enhanced simplification, is especially amenable to intersection-based learning, as in recursive learning and the method of Stålmarck. Experiments support the idea that problem variables can be eliminated and search trees can be shrunk by incorporating learning in the form of Boolean-ring saturation.