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We offer a new understanding of some aspects of practical SAT-solvers thatare based on DPLL with unit-clause propagation, clause-learning, and restarts.We do so by analyzing a concrete algorithm which we claim is faithful to whatpractical solvers do. In particular, before making any new decision or restart,the solver repeatedly applies the unit-resolution rule until saturation, andleaves no component to the mercy of non-determinism except for some internalrandomness. We prove the perhaps surprising fact that, although the solver isnot explicitly designed for it, with high probability it ends up behaving aswidth-k resolution after no more than O(n^2k+2) conflicts and restarts, where nis the number of variables. In other words, width-k resolution can be thoughtof as O(n^2k+2) restarts of the unit-resolution rule with learning.

Clause-Learning Algorithms with Many Restarts and Bounded-Width Resolution