Kolmogorov complexity for possibly infinite computations

Autores
Figueira, Santiago; Becher, Verónica
Año de publicación
2003
Idioma
inglés
Tipo de recurso
documento de conferencia
Estado
versión publicada
Descripción
In this paper we study a variant of the Kolmogorov complexity for non-effective computations, that is, either halting or non-halting computations on Turing machines. This complexity function is defined as the length of the shortest inputs that produce a desired output via a possibly non-halting computation. Clearly this function gives a lower bound of the classical Kolmogorov complexity. In particular, if the machine is allowed to overwrite its output, this complexity coincides with the classical Kolmogorov complexity for halting computations relative to the first jump of the halting problem. However, on machines that cannot erase their output –called monotone machines–, we prove that our complexity for non effective computations and the classical Kolmogorov complexity separate as much as we want. We also consider the prefix-free complexity for possibly infinite computations. We study several properties of the graph of these complexity functions and specially their oscillations with respect to the complexities for effective computations.
Eje: Teoría (TEOR)
Red de Universidades con Carreras en Informática (RedUNCI)
Materia
Ciencias Informáticas
Computational logic
Connection machines
Kolmogorov complexity
Program-size complexity
Turing machines
monotone machines
infinite computations
non-effective computations
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/22767

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network_name_str SEDICI (UNLP)
spelling Kolmogorov complexity for possibly infinite computationsFigueira, SantiagoBecher, VerónicaCiencias InformáticasComputational logicConnection machinesKolmogorov complexityProgram-size complexityTuring machinesmonotone machinesinfinite computationsnon-effective computationsIn this paper we study a variant of the Kolmogorov complexity for non-effective computations, that is, either halting or non-halting computations on Turing machines. This complexity function is defined as the length of the shortest inputs that produce a desired output via a possibly non-halting computation. Clearly this function gives a lower bound of the classical Kolmogorov complexity. In particular, if the machine is allowed to overwrite its output, this complexity coincides with the classical Kolmogorov complexity for halting computations relative to the first jump of the halting problem. However, on machines that cannot erase their output –called monotone machines–, we prove that our complexity for non effective computations and the classical Kolmogorov complexity separate as much as we want. We also consider the prefix-free complexity for possibly infinite computations. We study several properties of the graph of these complexity functions and specially their oscillations with respect to the complexities for effective computations.Eje: Teoría (TEOR)Red de Universidades con Carreras en Informática (RedUNCI)2003-10info:eu-repo/semantics/conferenceObjectinfo:eu-repo/semantics/publishedVersionObjeto de conferenciahttp://purl.org/coar/resource_type/c_5794info:ar-repo/semantics/documentoDeConferenciaapplication/pdf1545-1556http://sedici.unlp.edu.ar/handle/10915/22767enginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/2.5/ar/Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Argentina (CC BY-NC-SA 2.5)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-03T10:27:58Zoai:sedici.unlp.edu.ar:10915/22767Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-03 10:27:58.768SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Kolmogorov complexity for possibly infinite computations
title Kolmogorov complexity for possibly infinite computations
spellingShingle Kolmogorov complexity for possibly infinite computations
Figueira, Santiago
Ciencias Informáticas
Computational logic
Connection machines
Kolmogorov complexity
Program-size complexity
Turing machines
monotone machines
infinite computations
non-effective computations
title_short Kolmogorov complexity for possibly infinite computations
title_full Kolmogorov complexity for possibly infinite computations
title_fullStr Kolmogorov complexity for possibly infinite computations
title_full_unstemmed Kolmogorov complexity for possibly infinite computations
title_sort Kolmogorov complexity for possibly infinite computations
dc.creator.none.fl_str_mv Figueira, Santiago
Becher, Verónica
author Figueira, Santiago
author_facet Figueira, Santiago
Becher, Verónica
author_role author
author2 Becher, Verónica
author2_role author
dc.subject.none.fl_str_mv Ciencias Informáticas
Computational logic
Connection machines
Kolmogorov complexity
Program-size complexity
Turing machines
monotone machines
infinite computations
non-effective computations
topic Ciencias Informáticas
Computational logic
Connection machines
Kolmogorov complexity
Program-size complexity
Turing machines
monotone machines
infinite computations
non-effective computations
dc.description.none.fl_txt_mv In this paper we study a variant of the Kolmogorov complexity for non-effective computations, that is, either halting or non-halting computations on Turing machines. This complexity function is defined as the length of the shortest inputs that produce a desired output via a possibly non-halting computation. Clearly this function gives a lower bound of the classical Kolmogorov complexity. In particular, if the machine is allowed to overwrite its output, this complexity coincides with the classical Kolmogorov complexity for halting computations relative to the first jump of the halting problem. However, on machines that cannot erase their output –called monotone machines–, we prove that our complexity for non effective computations and the classical Kolmogorov complexity separate as much as we want. We also consider the prefix-free complexity for possibly infinite computations. We study several properties of the graph of these complexity functions and specially their oscillations with respect to the complexities for effective computations.
Eje: Teoría (TEOR)
Red de Universidades con Carreras en Informática (RedUNCI)
description In this paper we study a variant of the Kolmogorov complexity for non-effective computations, that is, either halting or non-halting computations on Turing machines. This complexity function is defined as the length of the shortest inputs that produce a desired output via a possibly non-halting computation. Clearly this function gives a lower bound of the classical Kolmogorov complexity. In particular, if the machine is allowed to overwrite its output, this complexity coincides with the classical Kolmogorov complexity for halting computations relative to the first jump of the halting problem. However, on machines that cannot erase their output –called monotone machines–, we prove that our complexity for non effective computations and the classical Kolmogorov complexity separate as much as we want. We also consider the prefix-free complexity for possibly infinite computations. We study several properties of the graph of these complexity functions and specially their oscillations with respect to the complexities for effective computations.
publishDate 2003
dc.date.none.fl_str_mv 2003-10
dc.type.none.fl_str_mv info:eu-repo/semantics/conferenceObject
info:eu-repo/semantics/publishedVersion
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http://purl.org/coar/resource_type/c_5794
info:ar-repo/semantics/documentoDeConferencia
format conferenceObject
status_str publishedVersion
dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/22767
url http://sedici.unlp.edu.ar/handle/10915/22767
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Argentina (CC BY-NC-SA 2.5)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Argentina (CC BY-NC-SA 2.5)
dc.format.none.fl_str_mv application/pdf
1545-1556
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instname:Universidad Nacional de La Plata
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reponame_str SEDICI (UNLP)
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instname_str Universidad Nacional de La Plata
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institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
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