On polynomial time bounded truth-table reducibility of NP sets to sparse sets
Mitsunori Ogiwara, Osamu Watanabe · 1990
We prove that if P ¢ NP, then there exists a set in NP that is polynomial time bounded truth-table reducible (in short, <Ptt-reducible) to no sparse set.In other words, we prove that no sparse <bPtt-hard set exists for NP unless P = NP.By using the technique proving this result, we investigate intractability of several number theoretic decision problems, i.e., decision problems defined naturally from number theoretic problems.We show that for those number theoretic decision problems, if it is not in P, then it is <~tt-reducible to no sparse set.