Relativizations of the P =? DNP Question for the BSS Model

We consider the uniform BSS model of computation where the machines can perform additions, multiplications, and tests of the form $xgeq 0$. 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

A topological view on algebraic computation models

We investigate the topological aspects of some algebraic computation models, in particular the BSS-model. Our results can be seen as bounds on how different BSS-computability and computability in the sense of computable analysis can be. The framework for this is Weihrauch reducibility. As a consequence of our characterizations, we establish that the solvability complexity index is (mostly) independent of the computational model, and that there thus is common ground in the study of non-computability between the BSS and TTE setting