Exponential-Time and Subexponential-Time Sets

Abstract In this paper, we prove that the symmetric difference of a ⩽ P k -parity -hard set for E and a subexponential-time-computable set is still ⩽ P k -parity -hard for E. This remains true for ⩽ P m -hard set for E since a 1-parity reduction is a many—one reduction. In addition, we show that this property fails to hold for some other types of reductions. We introduce and study the notions of E-complete kernel and E-hard kernel.

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