Computing with Colored Tangles

Computing with Colored Tangles

We suggest a diagrammatic model of computation based on an axiom of distributivity. A diagram of a decorated colored tangle, similar to those that appear in low dimensional topology, plays the role of a circuit diagram. Equivalent diagrams represent bisimilar computations. We prove that our model of...

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Bibliographic Details
Main Authors: Avishy Y. Carmi, Daniel Moskovich
Format: Article
Language:English
Published: MDPI AG 2015-07-01
Series:Symmetry
Subjects:
diagrammatic algebra
low dimensional topology
computation
Turing machine
interactive proof
Online Access:http://www.mdpi.com/2073-8994/7/3/1289
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spelling doaj-c19c52dc76b947139ab8ce2f2e6744ce2020-11-24T23:22:21ZengMDPI AGSymmetry2073-89942015-07-01731289133210.3390/sym7031289sym7031289Computing with Colored TanglesAvishy Y. Carmi0Daniel Moskovich1Faculty of Engineering Sciences & Center for Quantum Information Science and Technology, Ben-Gurion University of the Negev, Beer-Sheva 8410501, IsraelFaculty of Engineering Sciences & Center for Quantum Information Science and Technology, Ben-Gurion University of the Negev, Beer-Sheva 8410501, IsraelWe suggest a diagrammatic model of computation based on an axiom of distributivity. A diagram of a decorated colored tangle, similar to those that appear in low dimensional topology, plays the role of a circuit diagram. Equivalent diagrams represent bisimilar computations. We prove that our model of computation is Turing complete and with bounded resources that it can decide any language in complexity class IP, sometimes with better performance parameters than corresponding classical protocols.http://www.mdpi.com/2073-8994/7/3/1289diagrammatic algebralow dimensional topologycomputationTuring machineinteractive proof
collection DOAJ
language English
format Article
sources DOAJ
author Avishy Y. Carmi
Daniel Moskovich
spellingShingle Avishy Y. Carmi
Daniel Moskovich
Computing with Colored Tangles
Symmetry
diagrammatic algebra
low dimensional topology
computation
Turing machine
interactive proof
author_facet Avishy Y. Carmi
Daniel Moskovich
author_sort Avishy Y. Carmi
title Computing with Colored Tangles
title_short Computing with Colored Tangles
title_full Computing with Colored Tangles
title_fullStr Computing with Colored Tangles
title_full_unstemmed Computing with Colored Tangles
title_sort computing with colored tangles
publisher MDPI AG
series Symmetry
issn 2073-8994
publishDate 2015-07-01
description We suggest a diagrammatic model of computation based on an axiom of distributivity. A diagram of a decorated colored tangle, similar to those that appear in low dimensional topology, plays the role of a circuit diagram. Equivalent diagrams represent bisimilar computations. We prove that our model of computation is Turing complete and with bounded resources that it can decide any language in complexity class IP, sometimes with better performance parameters than corresponding classical protocols.
topic diagrammatic algebra
low dimensional topology
computation
Turing machine
interactive proof
url http://www.mdpi.com/2073-8994/7/3/1289
work_keys_str_mv AT avishyycarmi computingwithcoloredtangles
AT danielmoskovich computingwithcoloredtangles
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