In this article we describe and evaluate optimized compact data structures for watching literals. Experiments with our SAT solver PicoSAT show that this low-level optimization not only saves memory, but also turns out to speed up the SAT solver considerably. We also discuss how to store proof traces compactly in memory and further unique features of PicoSAT including an aggressive restart schedule. Keywords: SAT solver, watched literals, occurrence lists, proof traces, restarts

The past decade has seen clause learning as the most successful algorithm for SAT instances arising from real-world applications. This practical success is accompanied by theoretical results showing clause learning as equivalent in power to resolution. There exist, however, problems that are intractable for resolution, for which clause-learning solvers are hence doomed. In this paper, we present extended clause learning, a practical SAT algorithm that surpasses resolution in power. Indeed, we prove that it is equivalent in power to extended resolution, a proof system strictly more powerful than resolution. Empirical results based on an initial implementation suggest that the additional theoretical power can indeed translate into substantial practical gains. 1.

Abstract. Compared to SAT, there is no simple concept of what a solution to a QBF problem is. Furthermore, as the series of QBF evaluations shows, the QBF solvers that are available often disagree. Thus, proof generation for QBF seems to be even more important than for SAT. In this paper we propose a new uniform proof format, which captures refutations and witnesses for a variety of QBF solvers, and is based on a novel extended resolution rule for QBF. Our experiments show the flexibility of this new format. We also identify shortcomings of our format and conjecture that a purely resolution based proof calculus is not powerful enough to trace the most efficient solvers. 1

We report initial results on shortening propositional resolution refutation proofs. This has an application in speeding up deductive reconstruction (in theorem provers) of large propositional refutations, such as those produced by SAT-solvers. Key words: Proof verification, Propositional refutations 1

We demonstrate a family of propositional formulas in conjunctive normal form so that a formula of size N requires size 2NΩ(1) to refute using the tree-like OBDD refutation system of Atserias, Kolaitis and Vardi [3] with respect to all variable orderings. The lower bound generalizes earlier lower bounds on OBDD-based proofs of unsatisfiability in that it applies for all variable orderings, it applies when the clauses are processed according to an arbitrary schedule, and it applies when variables are eliminated via quantification. Current symbolic quantifier elimination algorithms for satisfiability generate tree-like proofs when run on unsatisfiable CNFs, so this lower bound applies to the run-times of these algorithms. 1

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We report initial results on shortening propositional resolution refutation proofs. This has an application in speeding up deductive reconstruction (in theorem provers) of large propositional refutations, such as those produced by SAT-solvers.