On γ-reducibility versus polynomial time many-one reducibility

Abstract

We prove that each element of a class of functions (denoted by NPC t P), whose graphs can be accepted in nondeterministic polynomial time, can be evaluated in deterministic polynomial time if and only if γ-reducibility is equivalent to polynomial time many-one reducibility. We also modify the proof technique used to obtain part of this result to obtain the stronger result that if every γ-reduction can be replaced by a polynomial time Turing reduction, then every function in NPC t P can be evaluated in deterministic polynomial time.