On polynomial time bounded truth-table reducibility of NP sets to sparse sets

Summary form only given. It is proved that if P not=NP, then there exits a set in NP that is polynomial-time bounded truth-table reducible to no sparse set. By using the technique proving this result, intractability of several number theoretic decision problems, i.e. decision problems defined naturally from number theoretic problems, is investigated. It is shown that for those number theoretic decision problems, if it is not in P, then it is polynomial-time bounded truth-table reducible to no sparse set.<
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