dc.contributor.author |
Calude, CS |
en |
dc.contributor.author |
Jain, S |
en |
dc.contributor.author |
Merkle, W |
en |
dc.contributor.author |
Stephan, F |
en |
dc.date.accessioned |
2018-07-18T04:42:53Z |
en |
dc.date.available |
2018-07-18T04:42:53Z |
en |
dc.date.issued |
2018-07-18 |
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dc.identifier.citation |
CDMTCS Research Reports CDMTCS-516 (2017) |
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dc.identifier.issn |
1178-3540 |
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dc.identifier.uri |
http://hdl.handle.net/2292/37503 |
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dc.description.abstract |
The Kolmogorov complexity of a string x is defined as the length of a shortest program p of x for some appropriate universal machine U, that is, U(p) = x and p is the shortest string with this property. Neither the plain nor
the prefix-free version of Kolmogorov complexity are recursive but for both versions it is well-known that there are recursive exact Solovay functions, that is, recursive upper bounds for Kolmogorov complexity that are infinitely
often tight. Let a coding function for a machine M be a function f such that f(x) is always a program of x for M. From the existence of exact Solovay functions it follows easily that for every universal machine there is a recursive coding function that maps infinitely many strings to a shortest program. Extending a recent line of research, in what follows it is investigated in which situations there is a coding function for some universal machine that maps infinitely many strings to a length-lexicographically least program. |
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dc.publisher |
Department of Computer Science, The University of Auckland, New Zealand |
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dc.relation.ispartofseries |
CDMTCS Research Report Series |
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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 |
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dc.source.uri |
https://www.cs.auckland.ac.nz/research/groups/CDMTCS/researchreports/index.php |
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dc.title |
Searching for Shortest and Least Programs |
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dc.type |
Technical Report |
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dc.subject.marsden |
Fields of Research |
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dc.rights.holder |
The author(s) |
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dc.rights.accessrights |
http://purl.org/eprint/accessRights/OpenAccess |
en |