Lower Bounds Are not Easier over the Reals: Inside PH (1999)
by
Hervé Fournier
,
Ecole Normale
,
Superieure Lyon
,
Unite Mixte
,
Recherche Cnrs-inria-ens Lyon
,
Pascal Koiran March
,
Pascal Koiran
| Citations: | 2 - 0 self |
BibTeX
@MISC{Fournier99lowerbounds,
author = {Hervé Fournier and Ecole Normale and Superieure Lyon and Unite Mixte and Recherche Cnrs-inria-ens Lyon and Pascal Koiran March and Pascal Koiran},
title = {Lower Bounds Are not Easier over the Reals: Inside PH},
year = {1999}
}
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Abstract
We prove that all NP problems over the reals with addition and order can be solved in polynomial time with the help of a boolean NP oracle. As a consequence, the "P = NP?" question over the reals with addition and order is equivalent to the classical question. For the reals with addition and equality only, the situation is quite different since P is known to be different from NP. Nevertheless, we prove similar transfer theorems for the polynomial hierarchy.
