TY - GEN

T1 - On polynomial time bounded truth-table reducibility of NP sets to sparse sets

AU - Ogiwara, Mitsunori

AU - Watanabe, Osamu

PY - 1990/1/1

Y1 - 1990/1/1

N2 - We prove that if P ≠ NP, then there exists a set in NP that is polynomial time bounded truth-table reducible (in short, ≤bttP-reducible) to no sparse set. In other words, we prove that no sparse ≤bttP-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 ≤bttP-reducible to no sparse set.

AB - We prove that if P ≠ NP, then there exists a set in NP that is polynomial time bounded truth-table reducible (in short, ≤bttP-reducible) to no sparse set. In other words, we prove that no sparse ≤bttP-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 ≤bttP-reducible to no sparse set.

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U2 - 10.1145/100216.100276

DO - 10.1145/100216.100276

M3 - Conference contribution

AN - SCOPUS:0025115364

SN - 0897913612

SN - 9780897913614

T3 - Proc 22nd Annu ACM Symp Theory Comput

SP - 457

EP - 467

BT - Proc 22nd Annu ACM Symp Theory Comput

PB - Publ by ACM

T2 - Proceedings of the 22nd Annual ACM Symposium on Theory of Computing

Y2 - 14 May 1990 through 16 May 1990

ER -