eT -reducibility of Sets

Semirecursive Sets and Positive Reducibility

Reducibility Classes of P-Selective Sets

A set is P-selective (Selman, 1979) if there is a polynomial-time semidecision algorithm for the set-an algorithm that given any two strings decides which is " more likely " to be in the set. This paper establishes a strict hierarchy among the various reductions and equivalences to P-selective sets. Given the large number of important problems that do not appear to have easy solutions, research...

Schnorr trivial sets and truth-table reducibility

We give several characterizations of Schnorr trivial sets, including a new lowness notion for Schnorr triviality based on truth-table reducibility. These characterizations allow us to see not only that some natural classes of sets, including maximal sets, are composed entirely of Schnorr trivials, but also that the Schnorr trivial sets form an ideal in the truth-table degrees but not the weak t...

Computably Enumerable Sets and Quasi-Reducibility

We consider the computably enumerable sets under the relation of Qreducibility. We first give several results comparing the upper semilattice of c.e. Q-degrees, 〈RQ,≤Q 〉, under this reducibility with the more familiar structure of the c.e. Turing degrees. In our final section, we use coding methods to show that the elementary theory of 〈RQ,≤Q 〉 is undecidable.

Relating Equivalence and Reducibility to Sparse Sets

For various polynomial-time reducibilities r, this paper asks whether being r-reducible to a sparse set is a broader notion than being r-equivalent to a sparse set. Although distinguishing equivalence and reducibility to sparse sets, for many-one or 1-truth-table reductions, would imply that P 6= NP, this paper shows that for k-truth-table reductions, k 2, equivalence and reducibility to sparse...