Abstract
We consider the following questions:
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1.
Can one compute satisfying assignments for satisfiable Boolean formulas in polynomial time with parallel queries to NP?
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2.
Is the unique optimal clique problem (UOCLIQUE) complete for PNP[O(log n)]?
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3.
Is the unique satisfiability problem (USAT) NP hard? We define 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 PNP[O(log n)]. We show that an affirmative answer to any of the three questions implies the existence of coNP checkable proofs for PNP[O(log n)] that can be generated in FP NP∥ . Furthermore, we construct an oracle relative to which there do not exist coNP checkable proofs for NP that are generated in FP NP∥ . It follows that relative to this oracle all of the above questions are answered negatively.
Part of this research was done while visiting the Univ. Politècnica de Catalunya in Barcelona. Partially supported by the Dutch foundation for scientific research (NWO) through NFI Project ALADDIN, under contract number NF 62-376.
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Buhrman, H., Thierauf, T. (1996). The complexity of generating and checking proofs of membership. In: Puech, C., Reischuk, R. (eds) STACS 96. STACS 1996. Lecture Notes in Computer Science, vol 1046. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60922-9_7
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DOI: https://doi.org/10.1007/3-540-60922-9_7
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