Some properties of exponential time complexity classes

The authors separate NE from P_x (NP), where x= n⁰⁽¹⁾-T. The class EXP-low[1] is introduced and applied in the investigations of stable properties for both EXP and NEXP hard sets. A set A is in EXP-low[1](EXP-low resp.) if EXP ^A[1]=EXP(EXP^A=EXP). The authors separate EXP-low[1] from EXP-low by constructing a set A such that EXP ^A[1]=EXP and EXP^A=EXP^EXP