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.
This research was supported in part by the National Science Foundation under grant MCS77-23493
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Selman, A.L. (1979). P-selective sets, tally languages, and the behavior of polynomial time reducibilities on NP. In: Maurer, H.A. (eds) Automata, Languages and Programming. ICALP 1979. Lecture Notes in Computer Science, vol 71. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09510-1_44
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DOI: https://doi.org/10.1007/3-540-09510-1_44
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