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.
['Richard Beigel', 'Lance Fortnow']
Are Cook and Karp ever the same