Single-tape and multi-tape Turing machines through the lens of the Grossone methodology

Journal of Supercomputing 65 (2):645-663 (2013)
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Abstract

The paper investigates how the mathematical languages used to describe and to observe automatic computations influence the accuracy of the obtained results. In particular, we focus our attention on Single and Multi-tape Turing machines which are described and observed through the lens of a new mathematical language which is strongly based on three methodological ideas borrowed from Physics and applied to Mathematics, namely: the distinction between the object (we speak here about a mathematical object) of an observation and the instrument used for this observation; interrelations holding between the object and the tool used for the observation; the accuracy of the observation determined by the tool. Results of the observation executed by the traditional and new languages are compared and discussed.

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Yaroslav Sergeyev
Università della Calabria

References found in this work

On Computable Numbers, with an Application to the Entscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.
Non-standard Analysis.Gert Heinz Müller - 1966 - Princeton University Press.
An Unsolvable Problem of Elementary Number Theory.Alonzo Church - 1936 - Journal of Symbolic Logic 1 (2):73-74.
The Consistency of the Continuum Hypothesis.Kurt Godel - 1940 - Princeton University Press.

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