Monte-Carlo style UCT search for boolean satisfiability

Abstract

In this paper, we investigate the feasibility of applying algorithms based on the Uniform Confidence bounds applied to Trees [12] to the satisfiability of CNF formulas. We develop a new family of algorithms based on the idea of balancing exploitation (depth-first search) and exploration (breadth-first search), that can be combined with two different techniques to generate random playouts or with a heuristics-based evaluation function. We compare our algorithms with a DPLL-based algorithm and with WalkSAT, using the size of the tree and the number of flips as the performance measure. While our algorithms perform on par with DPLL on instances with little structure, they do quite well on structured instances where they can effectively reuse information gathered from one iteration on the next. We also discuss the pros and cons of our different algorithms and we conclude with a discussion of a number of avenues for future work. © 2011 Springer-Verlag Berlin Heidelberg.