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An application of the Deutsch-Jozsa algorithm to formal languages and the word problem in groups

Lookup NU author(s): Dr Michael Batty, Dr Andrew Duncan, Professor Sarah Rees

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Abstract

We adapt the Deutsch-Jozsa algorithm to the context of formal language theory. Specifically, we use the algorithm to distinguish between trivial and nontrivial words in groups given by finite presentations, under the promise that a word is of a certain type. This is done by extending the original algorithm to functions of arbitrary length binary output, with the introduction of a more general concept of parity. We provide examples in which properties of the algorithm allow to reduce the number of oracle queries with respect to the deterministic classical case. This has some consequences for the word problem in groups with a particular kind of presentation. © 2008 Springer Berlin Heidelberg.


Publication metadata

Author(s): Batty M, Casaccino A, Duncan AJ, Rees S, Severini S

Editor(s): Kawano, Y., Mosca, M.

Publication type: Conference Proceedings (inc. Abstract)

Publication status: Published

Conference Name: Theory of Quantum Computation, Communication, and Cryptography: Third Workshop (TQC)

Year of Conference: 2008

Pages: 57-69

ISSN: 0302-9743 (Print) 1611-3349 (Online)

Publisher: Springer

URL: http://dx.doi.org/10.1007/978-3-540-89304-2_6

DOI: 10.1007/978-3-540-89304-2_6

Library holdings: Search Newcastle University Library for this item

Series Title: Lecture Notes in Computer Science

ISBN: 9783540893035


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