Towards a theory of infinite time blum-shub-smale machines

Authors:
Peter Koepke;Benjamin Seyfferth
Affiliations:
Mathematisches Institut, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany;Mathematisches Institut, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany
Venue:
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
Year:
2012

Citing 3
Cited 0

Computable analysis: an introduction

Computable analysis: an introduction
An Enhanced Theory of Infinite Time Register Machines

CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Infinite time register machines

CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers

Quantified Score

Hi-index	0.00

Visualization

Abstract

We introduce a generalization of Blum-Shub-Smale machines on the standard real numbers ℝ that is allowed to run for a transfinite ordinal number of steps before terminating. At limit times, register contents are set to the ordinary limit of previous register contents in ℝ. It is shown that each such machine halts before time ωω or diverges. We undertake first steps towards estimating the computational strength of these new machines.