Selectivity

A set is P-selective if there is a polynomial-time (p-time) semi-decision algorithm for the set-an algorithm that, given any two strings, decides which is "more likely" to be in the set. This paper studies two natural generalizations of P-selectivity: the NP-selective sets and the sets reducible to P-selective sets via p-time reductions. We show that even NP-selective sets are unlikely to be NP-complete, and we establish a strict hierarchy among the various reductions to P-selective sets.<>