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    The complexity of small universal Turing machines: A survey


    Woods, Damien and Neary, Turlough (2009) The complexity of small universal Turing machines: A survey. Theoretical Computer Science, 410 (4-5). pp. 443-450. ISSN 0304-3975

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    Abstract

    We survey some work concerned with small universal Turing machines, cellular automata, tag systems, and other simple models of computation. For example, it has been an open question for some time as to whether the smallest known universal Turing machines of Minsky, Rogozhin, Baiocchi and Kudlek are efficient (polynomial time) simulators of Turing machines. These are some of the most intuitively simple computational devices and previously the best known simulations were exponentially slow. We discuss recent work that shows that these machines are indeed efficient simulators. As a related result, we also find that Rule 110, a well-known elementary cellular automaton, is also efficiently universal. We also review a large number of old and new universal program size results, including new small universal Turing machines and new weakly, and semi-weakly, universal Turing machines. We then discuss some ideas for future work arising out of these, and other, results.

    Item Type: Article
    Keywords: Small universal Turing machines; Computational complexity; Polynomial time; Simulation; Tag systems; Cellular automata;
    Academic Unit: Faculty of Science and Engineering > Computer Science
    Faculty of Science and Engineering > Research Institutes > Hamilton Institute
    Item ID: 12413
    Identification Number: https://doi.org/10.1016/j.tcs.2008.09.051
    Depositing User: Damien Woods
    Date Deposited: 13 Feb 2020 12:20
    Journal or Publication Title: Theoretical Computer Science
    Publisher: Elsevier
    Refereed: Yes
    URI:

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