Minimal Degrees for Honest Polynomial Reducibilities
نویسنده
چکیده
The existence of minimal degrees is investigated for several polynomial reducibilities. It is shown that no set has minimal degree with respect to polynomial many-one or Turing reducibility. This extends a result. of Ladner [L] whew reciirsive sets are considered. An "honest '' polynomial reducibility, < ; , is defined which is a strengthening of polynomial Turing reduc-ibility. We prove that no recursive set, (or r.e. and P-immune set) has minimal < ;-degree. However. proving this same fact for all sets (or even all 3 ; sets) would imply P 2 .y/l. Finally, a partial converse of this result is obtained, proving that if a certain class of one-way functions exists then no set has minimal ;-degree.
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