Search-Space Pruning with Int-Splits for Faster QBF Solving

Abstract

In many QBF encodings, sequences of Boolean variables stand for binary representations of integer variables. Examples are state labels in bounded model checking or actions in planning problems. Often not the full possible range is used, e.g., for representing six different states, three Boolean variables are required, rendering two of the eight possible assignments irrelevant for the solution of the problem. As QBF solvers do not have any domain-specific knowledge on the formula they process, they are not able to detect this pruning opportunity. In this paper, we introduce the idea of int-splits, which provide domain-specific information on integer variables to QBF solvers. This is particularly appealing for parallel Divide-and-Conquer solving which partitions the search space into independently solvable sub-problems. Using this technique, we reduce the number of generated sub-problems from a full expansion to only the required subset. We then evaluate how many resources int-splits save in problems already well suited for D&C. In that context, we provide a reference implementation that splits QBF formulas into many sub-problems with or without int-splits and merges results. We finally propose a comment-based optional syntax extension to (Q)DIMACS that includes int-splits and is suited for supplying proposed guiding paths natively to D&C solvers.