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The Grossone Methodology Perspective on Turing Machines

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Automata, Universality, Computation

Part of the book series: Emergence, Complexity and Computation ((ECC,volume 12))

Abstract

This chapter discusses how the mathematical language used to describe and to observe automatic computations influences the accuracy of the obtained results. The chapter presents results obtained by describing and observing different kinds ofTuringmachines (single andmulti-tape, deterministic and non-deterministic) through the lens of a new mathematical language named Grossone. This emerging language is strongly based on threemethodological ideas borrowed from Physics and applied toMathematics: the distinction between the object (indeedmathematical 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. In the chapter, the new results are compared to those achievable by using traditional languages. It is shown that both languages do not contradict each other but observe and describe the same object (Turingmachines) but with different accuracies.

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Author information

Authors and Affiliations

  1. Dipartimento di Ingegneria Informatica, Modellistica, Elettronica e Sistemistica (DIMES), Università della Calabria, Rende, CS, Italy

    Yaroslav D. Sergeyev

  2. N.I. Lobatchevsky State University, Nizhni Novgorod, Russia

    Yaroslav D. Sergeyev

  3. Istituto di Calcolo e Reti ad Alte Prestazioni, C.N.R., Rende, CS, Italy

    Yaroslav D. Sergeyev

  4. Dipartimento di Ingegneria Informatica, Modellistica, Elettronica e Sistemistica (DIMES), Universitá della Calabria, Rende, CS, Italy

    Alfredo Garro

Authors
  1. Yaroslav D. Sergeyev
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  2. Alfredo Garro
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Editors and Affiliations

  1. Unconventional Computing Centre, University of the West of England, Bristol, United Kingdom

    Andrew Adamatzky

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Sergeyev, Y.D., Garro, A. (2015). The Grossone Methodology Perspective on Turing Machines. In: Adamatzky, A. (eds) Automata, Universality, Computation. Emergence, Complexity and Computation, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-319-09039-9_7

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  • DOI: https://doi.org/10.1007/978-3-319-09039-9_7

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09038-2

  • Online ISBN: 978-3-319-09039-9

  • eBook Packages: EngineeringEngineering (R0)

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