P-selective self-reducibles sets: a new characterization of P

Abstract

It is shown that any p-selective and self-reducible sets is in P. As the converse is also true, the authors obtain a new characterization of the class P. A generalization and several consequences of this theorem are discussed. Among other consequences, it is shown that under reasonable assumptions autoreducibility and self-reducibility differ on NP, and there are non-p-T-mitotic sets in NP.<>