Refutation of random constraint satisfaction problems using the sum of squares proof system
نویسنده
چکیده
Given a k-ary predicate P, a random instance of a constraint satisfaction problem with predicate P (CSP(P)) is a set of m constraints on n variables. Each constraint is P applied to k random literals. Such an instance is unsatisfiable with high probability when m >> n. Refutation is certifying that a given randomly chosen instance is unsatisfiable. This task has applications in cryptography, hardness of approximation, and learning theory. This thesis studies refutation using sum-of-squares (SOS) proof systems. SOS is a sequence of increasingly powerful proof systems parameterized by degree: the higher the degree, the more powerful the proof system. On the other hand, finding an SOS proof requires time exponential in the degree.
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