P-selective sets, tally languages, and the behavior of polynomial time reducibilities on NP

Abstract

The notion of p-selective sets, and tally languages, are used to study polynomial time reducibilities on NP. P-selectivity has the property that a set A belongs to the class P if and only if both Ā ≤Pm A and A is p-selective. We prove that for every tally language set in NP there exists a polynomial time equivalent set in NP that is p-selective. From this result it follows that if NEXT ≠ DEXT, then polynomial time Turing and many-one reducibilities differ on NP.