We study and compare in two degree-theoretic ways (iterated Halting oracles analogous to Kleene's arithmetical hierarchy and the Borel hierarchy of descriptive set theory) the capabilities and limitations of three models of analytic computation: BSS machines (aka real-RAM) and strongly/weakly analytic machines as introduced by Hotz et. al. (1995).
Cite
@article{arxiv.1006.0398,
title = {Real Analytic Machines and Degrees},
author = {Tobias Gärtner and Martin Ziegler},
journal= {arXiv preprint arXiv:1006.0398},
year = {2015}
}
Comments
20 pages. A preliminary version of this work had appeared in Proc. CCA 2011, EPTCS vol.24, arXiv:1006.0398v1