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

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


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.



External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Infinite Time Turing Machines With Only One Tape.D. E. Seabold & J. D. Hamkins - 2001 - Mathematical Logic Quarterly 47 (2):271-287.
Super Turing-machines.Jack Copeland - 1998 - Complexity 4 (1):30-32.
Infinite time Turing machines.Joel David Hamkins - 2002 - Minds and Machines 12 (4):567-604.
Infinite time Turing machines.Joel David Hamkins & Andy Lewis - 2000 - Journal of Symbolic Logic 65 (2):567-604.
Computable Diagonalizations and Turing’s Cardinality Paradox.Dale Jacquette - 2014 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 45 (2):239-262.
Is the human mind a Turing machine?D. King - 1996 - Synthese 108 (3):379-89.
Logically possible machines.Eric Steinhart - 2002 - Minds and Machines 12 (2):259-280.
Lagrange Lecture: Methodology of numerical computations with infinities and infinitesimals.Yaroslav Sergeyev - 2010 - Rendiconti Del Seminario Matematico dell'Università E Del Politecnico di Torino 68 (2):95–113.
Transcending Turing computability.B. J. Maclennan - 2003 - Minds and Machines 13 (1):3-22.


Added to PP

3,211 (#1,291)

6 months
440 (#817)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

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.

View all 29 references / Add more references