The Complexity of Generating and CheckingProofs of
نویسنده
چکیده
We consider the following questions: 1. Can one compute satisfying assignments for satissable Boolean formulas in polynomial time with parallel queries to NP? 2. Is the unique optimal clique problem (UOCLIQUE) complete for P NPO(log n)] ? 3. Is the unique satissability problem (USAT) NP hard? We deene a framework that enables us to study the complexity of generating and checking proofs of membership. We connect the above three questions to the complexity of generating and checking proofs of membership for sets in NP and P NPO(log n)]. We show that an aarmative answer to any of the three questions implies the existence of coNP checkable proofs for P NPO(log n)] that can be generated in FP NP k. Furthermore, we construct an oracle relative to which there do not exist coNP checkable proofs for NP that are generated in FP NP k. It follows that relative to this oracle all of the above questions are answered negatively.
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