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

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## 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 ≤ _{m} ^{P} 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.

## Keywords

Polynomial Time Turing Machine Conjunctive Normal Form Polynomial Time Reducibility Polynomial Time Computable Function
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© Springer-Verlag Berlin Heidelberg 1979