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Advances in Unconventional ComputingTwo Small Universal Reversible Turing Machines

Advances in Unconventional Computing: Two Small Universal Reversible Turing Machines [We study the problem of constructing small universal Turing machines (UTMs) under the constraint of reversibility, which is a property closely related to physical reversibility. Let URTM(m,n) denote an m-state n-symbol universal reversible Turing machine (URTM). Then, the problem is to find URTM(m,n) with small m and n. So far, several kinds of small URTMs have been given. Here, we newly construct two small URTMs. They are URTM(13,7) and URTM(10,8) that can simulate cyclic tag systems, a kind of universal string rewriting systems proposed by Cook. We show how these URTMs can be designed, and compare them with other existing URTMs.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Advances in Unconventional ComputingTwo Small Universal Reversible Turing Machines

Part of the Emergence, Complexity and Computation Book Series (volume 22)
Editors: Adamatzky, Andrew
Morita, Kenichi
Advances in Unconventional Computing — Jul 19, 2016
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16 pages

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Publisher
Springer International Publishing
Copyright
© Springer International Publishing Switzerland 2017
ISBN
978-3-319-33923-8
Pages
221 –237
DOI
10.1007/978-3-319-33924-5_10
Publisher site
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Abstract

[We study the problem of constructing small universal Turing machines (UTMs) under the constraint of reversibility, which is a property closely related to physical reversibility. Let URTM(m,n) denote an m-state n-symbol universal reversible Turing machine (URTM). Then, the problem is to find URTM(m,n) with small m and n. So far, several kinds of small URTMs have been given. Here, we newly construct two small URTMs. They are URTM(13,7) and URTM(10,8) that can simulate cyclic tag systems, a kind of universal string rewriting systems proposed by Cook. We show how these URTMs can be designed, and compare them with other existing URTMs.]

Published: Jul 19, 2016

Keywords: Turing Machine; Production Rule; Reversibility Condition; Uppercase Letter; Phase Marker

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