It is proved that if P ≠ NP, then there exists a set in NP that is not polynomial-time bounded truth-table reducible (in short, ≤bttP-reducible) to any sparse set. In other words, it is proved that no sparse ≤bttP-hard set exists for NP unless P = NP. By using the technique proving this result, the intractability of several number-theoretic decision problems, i.e., decision problems defined naturally from number-theoretic problems is investigated. It is shown that for these number-theoretic decision problems, if it is not in P, then it is not ≤bttP-reducible to any sparse set.
ASJC Scopus subject areas
- Computer Science(all)