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The Complexity of Small Universal Turing Machines: A Survey

  • Turlough Neary
  • Damien Woods
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7147)

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. In addition, another related result shows that Rule 110, a well-known elementary cellular automaton, is efficiently universal. We also discuss some old and new universal program size results, including the smallest known universal Turing machines. We finish the survey with results on generalised and restricted Turing machine models including machines with a periodic background on the tape (instead of a blank symbol), multiple tapes, multiple dimensions, and machines that never write to their tape. We then discuss some ideas for future work.

Keywords

Cellular Automaton Turing Machine Transition Rule Time Overhead Program Size 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Turlough Neary
    • 1
  • Damien Woods
    • 2
  1. 1.School of Computer Science & InformaticsUniversity College DublinIreland
  2. 2.Division of Engineering & Applied ScienceCalifornia Institute of TechnologyPasadenaUSA

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