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Seeking Practical CDCL Insights from Theoretical SAT Benchmarks

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Seeking Practical CDCL Insights from Theoretical SAT Benchmarks
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28
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CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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Over the last decades Boolean satisfiability (SAT) solvers based on conflict-driven clause learning (CDCL) have developed to the point where they can handle formulas with millions of variables. Yet a deeper understanding of how these solvers can be so successful has remained elusive. In this work we try to shed light on CDCL performance by using theoretical benchmarks. While these are crafted instances, they have the attractive features of being a) scalable, b) extremal with respect to different proof search parameters, and c) theoretically *easy* in the sense of having short proofs in the resolution proof system underlying CDCL. This allows for a systematic study of solver heuristics and how successfully they implement efficient proof search. We report results from extensive experiments with different CDCL parameter configurations on a wide range of benchmarks. Our findings include several examples where theory predicts and explains CDCL behaviour, but also raises a number of intriguing questions for further study.