Abstract
The notion ofp-selective sets, and tally languages, are used to study polynomial time reducibilities onNP. P-selectivity has the property that a setA belongs to the classP if and only if bothĀ ≤ p m A andA isp-selective. We prove that for every tally language set inNP there exists a polynomial time equivalent set inNP that isp-selective. From this result it follows that if NEXT ≠ DEXT, then polynomial time Turing and many-one reducibilities differ onNP.
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This research was supported in part by the National Science Foundation under grant MCS 77-23493
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Selman, A.L. P-selective sets, tally languages, and the behavior of polynomial time reducibilities onNP . Math. Systems Theory 13, 55–65 (1979). https://doi.org/10.1007/BF01744288
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DOI: https://doi.org/10.1007/BF01744288