An investigation of some theoretical aspects of reversible computing

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dc.contributor.advisorCockett, Robin
dc.contributor.authorGiles, Brett
dc.date.accessioned2014-11-05T21:01:10Z
dc.date.available2015-02-23T08:00:29Z
dc.date.issued2014-11-05
dc.date.submitted2014en
dc.description.abstractThe categorical semantics of reversible computing must be a category which combines the concepts of partiality and the ability to reverse any map in the category. Inverse categories, restriction categories in which each map is a partial isomorphism, provide exactly this structure. This thesis explores inverse categories and relates them to both quantum computing and standard non-reversible computing. The former is achieved by showing that commutative Frobenius algebras form an inverse category. The latter is by establishing the equivalence of the category of discrete inverse categories to the category of discrete Cartesian restriction categories — this is the main result of this thesis. This allows one to transfer the formulation of computability given by Turing categories onto discrete inverse categories.en_US
dc.identifier.citationGiles, B. (2014). An investigation of some theoretical aspects of reversible computing (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/24917en_US
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/24917
dc.identifier.urihttp://hdl.handle.net/11023/1941
dc.language.isoeng
dc.publisher.facultyGraduate Studies
dc.publisher.institutionUniversity of Calgaryen
dc.publisher.placeCalgaryen
dc.rightsUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.
dc.subjectComputer Science
dc.subject.classificationReversible Computingen_US
dc.subject.classificationInverse Categoriesen_US
dc.subject.classificationRestriction Categoriesen_US
dc.subject.classificationFrobenius Algebrasen_US
dc.subject.classificationProgramming Language Semanticsen_US
dc.titleAn investigation of some theoretical aspects of reversible computing
dc.typedoctoral thesis
thesis.degree.disciplineComputer Science
thesis.degree.grantorUniversity of Calgary
thesis.degree.nameDoctor of Philosophy (PhD)
ucalgary.item.requestcopytrue
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