Real Analytic Machines and Degrees
Tobias G\"artner (Universit\"at des Saarlandes), Martin Ziegler (TU, Darmstadt)
TL;DR
This paper compares the computational power and limitations of various models of real analytic computation using degree-theoretic methods, focusing on BSS machines and analytic machines.
Contribution
It introduces a degree-theoretic framework to analyze and compare different models of analytic computation, extending prior work on BSS and analytic machines.
Findings
Different models exhibit distinct degrees of computational power.
Degree-theoretic methods reveal limitations of analytic machines.
Comparison with classical hierarchies clarifies the capabilities of each model.
Abstract
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).
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