Self-reducible sets and some low sets, including p-selective sets, and weakly p-selective
sets are studied. Several different formulations of self-reducible sets are given and …

We show that any p-selective and self-reducible set is in P. As the converse is also true, we
obtain a new characterization of the class P. A generalization and several consequences of …

P-selective sets are used to distinguish polynomial time-bounded reducibilities on NP. In
particular, we consider different kinds of “positive” reductions; these preserve membership in …

The existence of sets not being≤ tt P-reducible to low sets is investigated for several
complexity classes such as UP, NP, the polynomial-time hierarchy, PSPACE, and EXPTIME …

In this note, we study NP-selective sets (formally, sets that are selective via NPSV t functions)
as a natural generalization of P-selective sets. We show that, assuming P≠ NP∩ coNP, the …

To every set A in NP we associate a (collection of) natural self-reducible set set(s). We prove
that every disjunctive-self-reducible set in NP is \leqq_d^P-equivalent to one of these natural …

Much structural work on NP-complete sets has exploited SAT′ s d-self-reducibility. In this
paper, we exploit the additional fact that SAT is a d-cylinder to show that NP-complete sets …

In this paper we discuss the relationship between certain structural properties of a set and
the set's computational complexity. We study four classes of sets for which the membership …

We distinguish self-reducibility of a languageLwith the question of whether search reduces
to decision forL. Results include:(i) If NE≠ E, then there exists a setLin NP− P such that …

Hartmanis and Berman have conjectured that all NP-complete sets are polynomial time
isomorphic. A consequence of the conjecture is that there are no sparse NP-complete sets …