Sum of squares lower bounds for refuting any CSP

  title={Sum of squares lower bounds for refuting any CSP},
  author={Pravesh Kothari and Ryuhei Mori and Ryan M O'Donnell and David Witmer},
Let <i>P</i>:{0,1}<sup><i>k</i></sup> → {0,1} be a nontrivial <i>k</i>-ary predicate. Consider a random instance of the constraint satisfaction problem (<i>P</i>) on <i>n</i> variables with Δ <i>n</i> constraints, each being <i>P</i> applied to <i>k</i> randomly chosen literals. Provided the constraint density satisfies Δ ≫ 1, such an instance is unsatisfiable with high probability. The <em>refutation</em> problem is to efficiently find a proof of unsatisfiability. We show that whenever… CONTINUE READING

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