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Maurice Margenstern’s Contributions to the Field of Small Universal Turing Machines

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Automata, Universality, Computation

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

Abstract

On the occasion of his 65th birthday we survey some of the work of Maurice Margenstern on small universal Turing machines. Margenstern has been one of the most prolific contributors to this field, having constructed numerous small universal programs for a number of Turing machine models. These positive results are complemented by Margenstern’s negative results, or lower bounds, on universal program size. Finally, he has even explored the space in-between the known program size upper and lower bounds by giving small programs that iterate the Collatz function, which suggests that proving negative results on programs of this size will be at least as hard as resolving the Collatz problem.

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Authors and Affiliations

  1. Institute for Neuroinformatics, University of Zürich and ETH Zürich, Zürich, Switzerland

    Turlough Neary

  2. California Institute of Technology, Pasadena, CA, 91125, USA

    Damien Woods

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  1. Turlough Neary
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  2. Damien Woods
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Correspondence to Turlough Neary .

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

    Andrew Adamatzky

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Neary, T., Woods, D. (2015). Maurice Margenstern’s Contributions to the Field of Small Universal 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_5

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  • DOI: https://doi.org/10.1007/978-3-319-09039-9_5

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09038-2

  • Online ISBN: 978-3-319-09039-9

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