Boolean Rings for Intersection-Based Satisfiability

Abstract

There is not a person in this courtroomwho has never told a lie, who has never done an immoral thing, and there is no man living who has never looked upon a woman without desire. 1 -Harper Lee: To Kill a MockingbirdAbstract. A potential advantage of using a Boolean-ring formalism for propositional formulae is the large measure of simplification it facilitates. We propose a combined linear and binomial representation for Booleanring 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.