Equivalence of Nc K and Ac Closures of Np and Other Classes
نویسنده
چکیده
Gottlob, (1993, in \Proceedings, 34th IEEE Symp. on Found. Comput. Sci.," pp. 42{ 51), showed that any set recognized by polynomial-size, log-depth trees with queries to SAT is p tt-reducible to NP. Based on his technique, it is shown for any set A and any k 1, that NC k (A) AC k?1 (R NP ctt (A)), where R NP ctt (A) is the NP ctt-closure of A. As a consequence, it is shown for any class C that is closed under NP ctt-reductions, such as NP and C = P, and for any k 1, that NC k (C) = AC k?1 (C), which resolves a question that has been left open for a long time.
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