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
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/22767
Ver los metadatos del registro completo
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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 Objeto de conferencia 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 |
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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) |
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openAccess |
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http://creativecommons.org/licenses/by-nc-sa/2.5/ar/ Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Argentina (CC BY-NC-SA 2.5) |
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application/pdf 1545-1556 |
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