We consider the uniform BSS model of computation where the machines can perform additions, multiplications, and tests of the form $x\geq 0$. The oracle machines can also check whether a tuple of real numbers belongs to a given oracle set ${\cal O}$ or not. We construct oracles such that the classes P and DNP relative to these oracles are equal or not equal.
@InProceedings{ganer:OASIcs.CCA.2009.2266, author = {Ga{\ss}ner, Christine}, title = {{Relativizations of the P =? DNP Question for the BSS Model}}, booktitle = {6th International Conference on Computability and Complexity in Analysis (CCA'09)}, pages = {141--148}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-939897-12-5}, ISSN = {2190-6807}, year = {2009}, volume = {11}, editor = {Bauer, Andrej and Hertling, Peter and Ko, Ker-I}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.CCA.2009.2266}, URN = {urn:nbn:de:0030-drops-22667}, doi = {10.4230/OASIcs.CCA.2009.2266}, annote = {Keywords: BSS machines, oracle machines, relativizations, P-DNP problem, real knapsack problem} }
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