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The monoidal structure of Turing machines†

Published online by Cambridge University Press:  28 February 2013

MIKLÓS BARTHA
MIKLÓS BARTHA*
Affiliation:
Department of Computer Science, Memorial University of Newfoundland St. John's, NL, Canada Email: bartha@inf.u-szeged.hu
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Abstract

Indexed monoidal algebras are introduced as an equivalent structure for self-dual compact closed categories, and a coherence theorem is proved for the category of such algebras. Turing automata and Turing graph machines are defined by generalising the classical Turing machine concept so that the collection of such machines becomes an indexed monoidal algebra. On the analogy of the von Neumann data-flow computer architecture, Turing graph machines are proposed as potentially reversible low-level universal computational devices, and a truly reversible molecular size hardware model is presented as an example.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 23 , Special Issue 2: Developments In Computational Models 2010 , April 2013 , pp. 204 - 246
Copyright
Copyright © Cambridge University Press 2013

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Footnotes

†

This work was partially supported by the Natural Science and Engineering Research Council of Canada.

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