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Approximate Outputs of Accelerated Turing Machines Closest to Their Halting Point

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Intelligent Information and Database Systems (ACIIDS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11431))

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Abstract

The accelerated Turing machine (ATM) which can compute super-tasks are devices with the same computational structure as Turing machines (TM) and they are also defined as the work-horse of hypercomputation. Is the final output of the ATM can be produced at the halting state? We supported our analysis by reasoning on Thomson’s paradox and by looking closely the result of the Twin Prime conjecture. We make sure to avoid unnecessary discussion on the infinite amount of space used by the machine or considering Thomson’s lamp machine, on the difficulty of specifying a machine’s outcome. Furthermore, it’s important for us that a clear definition counterpart for ATMs of the non-halting/halting dichotomy for classical Turing must be introduced. Considering a machine which has run for a countably infinite number of steps, this paper addresses the issue of defining the output of a machine close or at the halting point.

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Acknowledgement

The work and the contribution were supported by the SPEV project “Smart Solutions in Ubiquitous Computing Environments”, 2019, University of Hradec Kralove, Faculty of Informatics and Management, Czech Republic.

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Authors and Affiliations

  1. Center for Basic and Applied Research, Faculty of Informatics and Management, University of Hradec Kralove, Rokitanskeho 62, 500 03, Hradec Kralove, Czech Republic

    Sebastien Mambou, Ondrej Krejcar & Ali Selamat

  2. Malaysia Japan International Institute of Technology (MJIIT), Universiti Teknologi Malaysia, Jalan Sultan Yahya Petra, Kuala Lumpur, Malaysia

    Ali Selamat

Authors
  1. Sebastien Mambou
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  2. Ondrej Krejcar
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  3. Ali Selamat
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Corresponding author

Correspondence to Ondrej Krejcar .

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Editors and Affiliations

  1. Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Ngoc Thanh Nguyen

  2. Bina Nusantara University, Jakarta, Indonesia

    Ford Lumban Gaol

  3. National University of Kaohsiung, Kaohsiung, Taiwan

    Tzung-Pei Hong

  4. Wrocław University of Science and Technology, Wrocław, Poland

    Bogdan Trawiński

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Mambou, S., Krejcar, O., Selamat, A. (2019). Approximate Outputs of Accelerated Turing Machines Closest to Their Halting Point. In: Nguyen, N., Gaol, F., Hong, TP., Trawiński, B. (eds) Intelligent Information and Database Systems. ACIIDS 2019. Lecture Notes in Computer Science(), vol 11431. Springer, Cham. https://doi.org/10.1007/978-3-030-14799-0_60

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  • DOI: https://doi.org/10.1007/978-3-030-14799-0_60

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-14798-3

  • Online ISBN: 978-3-030-14799-0

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