Self-Reducible, P-Selective, Near-Testable, and P-Cheatable Sets: The Effect of Internal Structure on the Complexity of a Set

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 question for one element of the domain can be related to the membership question of other smaller (w.r.t. some ordering) elements: self-reducible sets, p-selective sets, near-testable sets and p-cheatable sets. The purpose of the paper is to suggest that a continuing systematic study of the relationship between this type of internal structure and the computational complexity of a set is in order. Although some new results are presented, much of the paper is an attempt to review know results and suggest unifying concepts.