Universal Reversible Turing Machines

  • Kenichi Morita
Part of the Monographs in Theoretical Computer Science. An EATCS Series book series (EATCS)


In this chapter, the problem of finding small universal Turing machines (UTMs) that satisfy the reversibility condition is studied. Such UTMs are called universal reversible Turing machines (URTMs). Let URTM(m,n) denote an m-state n-symbol URTM.We give several URTM(m,n)’s with small m and n. Here, a method of simulating cyclic tag systems (CTSs) by URTMs is employed. A CTS is a kind of a very simple string rewriting system, and is known to be computationally universal. By this method, URTM(10,8), URTM(13,7), URTM(15,6), URTM(17,5), URTM(24,4), and URTM(32,3) are obtained. On the other hand, it is generally difficult to design small reversible TMs with two symbols or with a very small number of states. For these cases, we apply general conversion methods to some of the above small URTMs, and obtain URTM(138,2), URTM(4,168), and URTM(3, 36654).


universal reversible Turing machine small universal Turing machine cyclic tag system 


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Copyright information

© Springer Japan KK 2017

Authors and Affiliations

  • Kenichi Morita
    • 1
  1. 1.Professor Emeritus, Hiroshima UniversityHiroshimaJapan

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