Spectral Representation of Some Computably Enumerable Sets With an Application to Quantum Provability

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dc.contributor.author Calude, CS en
dc.contributor.author Tadaki, K en
dc.date.accessioned 2014-01-05T22:48:15Z en
dc.date.available 2014-01-05T22:48:15Z en
dc.date.issued 2013 en
dc.identifier.citation CDMTCS Research Reports CDMTCS-434 (2013) en
dc.identifier.issn 1178-3540 en
dc.identifier.uri http://hdl.handle.net/2292/21333 en
dc.description.abstract We propose a new type of quantum computer which is used to prove a spectral representation for a class S of computable sets. When S ∈ S codes the theorems of a formal system, the quantum computer produces through measurement all theorems and proofs of the formal system. We conjecture that the spectral representation is valid for all computably enumerable sets. The conjecture implies that the theorems of a general formal system, like Peano Arithmetic or ZFC, can be produced through measurement; however, it is unlikely that the quantum computer can produce the proofs as well, as in the particular case of S. The analysis suggests that showing the provability of a statement is different from writing up the proof of the statement. en
dc.publisher Department of Computer Science, The University of Auckland, New Zealand en
dc.relation.ispartofseries CDMTCS Research Report Series en
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. en
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en
dc.source.uri http://www.cs.auckland.ac.nz/staff-cgi-bin/mjd/secondcgi.pl?serial en
dc.title Spectral Representation of Some Computably Enumerable Sets With an Application to Quantum Provability en
dc.type Technical Report en
dc.subject.marsden Fields of Research::280000 Information, Computing and Communication Sciences en
dc.rights.holder The author(s) en
dc.rights.accessrights http://purl.org/eprint/accessRights/OpenAccess en

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