Small Semi-weakly Universal Turing Machines

  • Damien Woods
  • Turlough Neary
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4664)

Abstract

We present two small universal Turing machines that have 3 states and 7 symbols, and 4 states and 5 symbols respectively. These machines are semi-weak which means that on one side of the input they have an infinitely repeated word and on the other side there is the usual infinitely repeated blank symbol. This work can be regarded as a continuation of early work by Watanabe on semi-weak machines. One of our machines has only 17 transition rules making it the smallest known semi-weakly universal Turing machine. Interestingly, our two machines are symmetric with Watanabe’s 7-state and 3-symbol, and 5-state and 4-symbol machines, even though we use a different simulation technique.

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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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