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A Survey of Infinite Time Turing Machines

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Machines, Computations, and Universality (MCU 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4664))

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Abstract

Infinite time Turing machines extend the operation of ordinary Turing machines into transfinite ordinal time, thereby providing a natural model of infinitary computability, with robust notions of computability and decidability on the reals, while remaining close to classical concepts of computability. Here, I survey the theory of infinite time Turing machines and recent developments. These include the rise of infinite time complexity theory, the introduction of infinite time computable model theory, the study of the infinite time analogue of Borel equivalence relation theory, and the introduction of new ordinal computational models. The study of infinite time Turing machines increasingly relies on the interaction of methods from set theory, descriptive set theory and computability theory.

Math Subject Codes: 03D30, 03D60, 03E15. Keywords: infinite time Turing machines, infinitary computability, ordinal computation. This article is adapted from an abstract of the same title written for the Bonn International Workshop on Ordinal Computation (BIWOC) 2007.

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References

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Authors and Affiliations

  1. The City University of New York,  

    Joel David Hamkins

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  1. Joel David Hamkins
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Jérôme Durand-Lose Maurice Margenstern

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Hamkins, J.D. (2007). A Survey of Infinite Time Turing Machines. In: Durand-Lose, J., Margenstern, M. (eds) Machines, Computations, and Universality. MCU 2007. Lecture Notes in Computer Science, vol 4664. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74593-8_5

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  • DOI: https://doi.org/10.1007/978-3-540-74593-8_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74592-1

  • Online ISBN: 978-3-540-74593-8

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