Simplicity via Provability for Universal Prefix-free Turing Machines

Simplicity via Provability for Universal Prefix-free Turing Machines

Universality is one of the most important ideas in computability theory. There are various criteria of simplicity for universal Turing machines. Probably the most popular one is to count the number of states/symbols. This criterion is more complex than it may appear at a first glance. In this note w...

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Main Author: Cristian S. Calude
Format: Article
Language:English
Published: Open Publishing Association 2009-06-01
Series:Electronic Proceedings in Theoretical Computer Science
Online Access:http://arxiv.org/pdf/0906.3235v1
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spelling doaj-d2ab347a7a1e4d0c90d2f2b4df1504712020-11-24T20:47:07ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802009-06-011Proc. CSP 2008162110.4204/EPTCS.1.2Simplicity via Provability for Universal Prefix-free Turing MachinesCristian S. CaludeUniversality is one of the most important ideas in computability theory. There are various criteria of simplicity for universal Turing machines. Probably the most popular one is to count the number of states/symbols. This criterion is more complex than it may appear at a first glance. In this note we review recent results in Algorithmic Information Theory and propose three new criteria of simplicity for universal prefix-free Turing machines. These criteria refer to the possibility of proving various natural properties of such a machine (its universality, for example) in a formal theory, PA or ZFC. In all cases some, but not all, machines are simple. http://arxiv.org/pdf/0906.3235v1
collection DOAJ
language English
format Article
sources DOAJ
author Cristian S. Calude
spellingShingle Cristian S. Calude
Simplicity via Provability for Universal Prefix-free Turing Machines
Electronic Proceedings in Theoretical Computer Science
author_facet Cristian S. Calude
author_sort Cristian S. Calude
title Simplicity via Provability for Universal Prefix-free Turing Machines
title_short Simplicity via Provability for Universal Prefix-free Turing Machines
title_full Simplicity via Provability for Universal Prefix-free Turing Machines
title_fullStr Simplicity via Provability for Universal Prefix-free Turing Machines
title_full_unstemmed Simplicity via Provability for Universal Prefix-free Turing Machines
title_sort simplicity via provability for universal prefix-free turing machines
publisher Open Publishing Association
series Electronic Proceedings in Theoretical Computer Science
issn 2075-2180
publishDate 2009-06-01
description Universality is one of the most important ideas in computability theory. There are various criteria of simplicity for universal Turing machines. Probably the most popular one is to count the number of states/symbols. This criterion is more complex than it may appear at a first glance. In this note we review recent results in Algorithmic Information Theory and propose three new criteria of simplicity for universal prefix-free Turing machines. These criteria refer to the possibility of proving various natural properties of such a machine (its universality, for example) in a formal theory, PA or ZFC. In all cases some, but not all, machines are simple.
url http://arxiv.org/pdf/0906.3235v1
work_keys_str_mv AT cristianscalude simplicityviaprovabilityforuniversalprefixfreeturingmachines
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