Combining satisfiability techniques from AI and OR

The recent effort to integrate techniques from the fields of artificial intelligence and operations research has been motivated in part by the fact that scientists in each group are often unacquainted with recent (and not so recent) progress in the other field. Our goal in this paper is to introduce the artificial intelligence community to pseudo-Boolean representation and cutting plane proofs, and to introduce the operations research community to restricted learning methods such as relevance-bounded learning. Complete methods for solving satisfiability problems are necessarily bounded from below by the length of the shortest proof of unsatisfiability; the fact that cutting plane proofs of unsatisfiability can be exponentially shorter than the shortest resolution proof can thus in theory lead to substantial improvements in the performance of complete satisfiability engines. Relevance-bounded learning is a method for bounding the size of a learned constraint set. It is currently the best artificial intelligence strategy for deciding which learned constraints to retain and which to discard. We believe these two elements or some analogous form of them are necessary ingredients to improving the performance of satisfiability algorithms generally. We also present a new cutting plane proof of the pigeonhole principle that is of size n², and show how to implement some intelligent backtracking techniques using pseudo-Boolean representation.