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The Complexity of Small Universal Turing Machines

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Computation and Logic in the Real World (CiE 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4497))

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Abstract

We survey some work concerned with small universal Turing machines, cellular automata, 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 mention some new universal program-size results, including new small universal Turing machines and new semi-weakly universal Turing machines. We then discuss some ideas for future work arising out of these, and other, results.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University College Cork, Ireland

    Damien Woods

  2. TASS, Department of Computer Science, National University of Ireland Maynooth, Ireland

    Turlough Neary

Authors
  1. Damien Woods
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  2. Turlough Neary
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Editor information

Editors and Affiliations

  1. Dept. of Pure Mathematics, University of Leeds, LS2 9JT, Leeds, UK

    S. Barry Cooper

  2. Institue for Logic, Language and Computation (ILLC), Universiteit van Amsterdam, Plantage Muidergracht 24, 1018, TV Amsterdam, The Netherlands

    Benedikt Löwe

  3. Dipartimento di Scienze Matematiche ed Informatiche “R. Magari”, University of Siena, 53100, Siena, Italy

    Andrea Sorbi

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Woods, D., Neary, T. (2007). The Complexity of Small Universal Turing Machines. In: Cooper, S.B., Löwe, B., Sorbi, A. (eds) Computation and Logic in the Real World. CiE 2007. Lecture Notes in Computer Science, vol 4497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73001-9_84

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  • DOI: https://doi.org/10.1007/978-3-540-73001-9_84

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73000-2

  • Online ISBN: 978-3-540-73001-9

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