Are Cook and Karp Ever the Same?

We consider the question whether there exists a set A such that every set polynomial-time Turing equivalent to A is also many-one equivalent to A. We show that if E = NE then no sparse set has this property. We give the first relativized world where there exists a set with this property, and in this world the set A is sparse.

• Type: Conference
• Year: 2003
• Where: COCO
• Authors: Richard Beigel, Lance Fortnow
• Keywords: COCO 2003, Set Polynomial-time, Sparse Set, first Relativized World