Heuristics for SAT algorithms: Searching for some foundations

A general model for (complete) SAT algorithms splitting a problem F into a nite number of sub-problems (F 1 ; : : : F m) is developed. The general scheme for \branching rules" is based on the notions of \potentials" and \projections" : By the potential diierences b i = (F) ? (F i) > 0 we measure some reduction in decision complexity, while the projection aggregates these numbers ~ b = (b 1 ; : : : ; b m) into one number (~ b) 0. A branching with minimal (~ b) is chosen. We derive some general results about potentials and projections, giving some ((rst) insights into the construction of useful potentials and projections. In the second part we present an implementation based on these ideas (performing full look-ahead and using autarkies), with a new, simple branching rule. Experimental results on the number of leaves in the search tree and the running times for random (3-7)-CNF at the (predicted) threshold are given.

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