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Efficient Algorithms for Semirandom Planted CSPs at the Refutation Threshold

Pravesh Kothari, Princeton University
E18-304

Abstract: We present an efficient algorithm to solve semi-random planted instances of any Boolean constraint satisfaction problem (CSP). The semi-random model is a hybrid between worst-case and average-case input models, where the input is generated by (1) choosing an arbitrary planted assignment x∗, (2) choosing an arbitrary clause structure, and (3) choosing literal negations for each clause from an arbitrary distribution "shifted by x∗" so that x∗ satisfies each constraint. For an n variable semi-random planted instance of a k-arity…

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