Ternary Max-Min algebra with application to reversible logic synthesis

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dc.contributor.authorKhan, Musharrat
dc.contributor.authorUniversity of Lethbridge. Faculty of Arts and Science
dc.contributor.supervisorRice, Jacqueline E.
dc.date.accessioned2017-05-01T21:15:51Z
dc.date.available2017-05-01T21:15:51Z
dc.date.issued2017
dc.degree.levelMastersen_US
dc.description.abstractTernary reversible circuits are 0.63 times more compact than equivalent binary reversible circuits and are suitable for low-power implementations. Two notable previous works on ternary reversible circuit synthesis are the ternary Galois field sum of products (TGFSOP) expression-based method and the ternary Max-Min algebra-based method. These methods require high quantum cost and large number of ancilla inputs. To address these problems we develop an alternative ternary Max-Min algebra-based method, where ternary logic functions are represented as Max-Min expressions and realized using our proposed multiple-controlled unary gates. We also show realizations of multiple-controlled unary gates using elementary quantum gates. We develop a method for minimization of ternary Max-Min expressions of up to four variables using ternary K-maps. Finally, we develop a hybrid Genetic Algorithm (HGA)-based method for the synthesis of ternary reversible circuits. The HGA has been tested with 24 ternary benchmark functions with up to five variables. On average our method reduces quantum cost by 41.36% and requires 35.72% fewer ancilla inputs than the TGFSOP-based method. Our method also requires 74.39% fewer ancilla inputs than the previous ternary Max-Min algebra-based method.en_US
dc.embargoNoen_US
dc.identifier.urihttps://hdl.handle.net/10133/4840
dc.language.isoen_USen_US
dc.proquest.subject0464en_US
dc.proquest.subject0984en_US
dc.proquestyesYesen_US
dc.publisherLethbridge, Alta : University of Lethbridge, Dept. of Mathematics and Computer Scienceen_US
dc.publisher.departmentDepartment of Mathematics and Computer Scienceen_US
dc.publisher.facultyArts and Scienceen_US
dc.relation.ispartofseriesThesis (University of Lethbridge. Faculty of Arts and Science)en_US
dc.subjectancilla inputsen_US
dc.subjectquantum costen_US
dc.subjectternary Max-Min algebraen_US
dc.subjectternary reversible circuitsen_US
dc.subjectunary gatesen_US
dc.titleTernary Max-Min algebra with application to reversible logic synthesisen_US
dc.typeThesisen_US
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