Lower Bounds Are Not Easier over the Reals: Inside PH

Authors:
Hervé Fournier;Pascal Koiran
Affiliations:
-;-
Venue:
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Year:
2000

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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.