The Complexity of Small Universal Turing Machines

  • Damien Woods
  • Turlough Neary
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4497)

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Damien Woods
    • 1
  • Turlough Neary
    • 2
  1. 1.Department of Computer Science, University College CorkIreland
  2. 2.TASS, Department of Computer Science, National University of Ireland MaynoothIreland

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