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.
Cite
CITATION STYLE
Fournier, H., & Koiran, P. (2000). Lower bounds are not easier over the reals: Inside PH. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1853, pp. 832–843). Springer Verlag. https://doi.org/10.1007/3-540-45022-x_70
Register to see more suggestions
Mendeley helps you to discover research relevant for your work.
