On fixed point theory in partially ordered sets and an application to asymptotic complexity of algorithms

The celebrated Kleene fixed point theorem is crucial in the mathematical modelling of recursive specifications in Denotational Semantics. In this paperwe discuss whether the hypothesis of the aforementioned result can be weakened. An affirmative answer to the aforesaid inquiry is provided so that a...

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Detalles Bibliográficos
Autores: Estevan, Asier, Miñana, Juan-José, Valero, Oscar
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Instituto de Salud Carlos III (ISCIII)
Repositorio:Repisalud
Idioma:inglés
OAI Identifier:oai:repisalud.isciii.es:20.500.12105/22817
Acceso en línea:https://hdl.handle.net/20.500.12105/22817
Access Level:acceso abierto
Palabra clave:Partial order
Quasi-metric
Fixed point
Kleene
Asymptotic complexity
Recurrence equation
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spelling On fixed point theory in partially ordered sets and an application to asymptotic complexity of algorithmsEstevan, AsierMiñana, Juan-JoséValero, OscarPartial orderQuasi-metricFixed pointKleeneAsymptotic complexityRecurrence equationThe celebrated Kleene fixed point theorem is crucial in the mathematical modelling of recursive specifications in Denotational Semantics. In this paperwe discuss whether the hypothesis of the aforementioned result can be weakened. An affirmative answer to the aforesaid inquiry is provided so that a characterization of those properties that a self-mapping must satisfy in order to guarantee that its set of fixed points is non-emptywhen no notion of completeness are assumed to be satisfied by the partially ordered set. Moreover, the case in which the partially ordered set is coming from a quasi-metric space is treated in depth. Finally, an application of the exposed theory is obtained. Concretely, a mathematical method to discuss the asymptotic complexity of those algorithms whose running time of computing fulfills a recurrence equation is presented. Moreover, the aforesaid method retrieves the fixed point basedmethods that appear in the literature for asymptotic complexity analysis of algorithms. However, our new method improves the aforesaid methods because it imposes fewer requirements than those that have been assumed in the literature and, in addition, it allows to state simultaneously upper and lower asymptotic bounds for the running time computing.Springer20242024-09-1020192019-10-0120192019-10-01research articlehttp://purl.org/coar/resource_type/c_2df8fbb1AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articlehttps://hdl.handle.net/20.500.12105/22817reponame:Repisaludinstname:Instituto de Salud Carlos III (ISCIII)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:repisalud.isciii.es:20.500.12105/228172026-06-12T12:43:37Z
dc.title.none.fl_str_mv On fixed point theory in partially ordered sets and an application to asymptotic complexity of algorithms
title On fixed point theory in partially ordered sets and an application to asymptotic complexity of algorithms
spellingShingle On fixed point theory in partially ordered sets and an application to asymptotic complexity of algorithms
Estevan, Asier
Partial order
Quasi-metric
Fixed point
Kleene
Asymptotic complexity
Recurrence equation
title_short On fixed point theory in partially ordered sets and an application to asymptotic complexity of algorithms
title_full On fixed point theory in partially ordered sets and an application to asymptotic complexity of algorithms
title_fullStr On fixed point theory in partially ordered sets and an application to asymptotic complexity of algorithms
title_full_unstemmed On fixed point theory in partially ordered sets and an application to asymptotic complexity of algorithms
title_sort On fixed point theory in partially ordered sets and an application to asymptotic complexity of algorithms
dc.creator.none.fl_str_mv Estevan, Asier
Miñana, Juan-José
Valero, Oscar
author Estevan, Asier
author_facet Estevan, Asier
Miñana, Juan-José
Valero, Oscar
author_role author
author2 Miñana, Juan-José
Valero, Oscar
author2_role author
author
dc.contributor.none.fl_str_mv
dc.subject.none.fl_str_mv Partial order
Quasi-metric
Fixed point
Kleene
Asymptotic complexity
Recurrence equation
topic Partial order
Quasi-metric
Fixed point
Kleene
Asymptotic complexity
Recurrence equation
description The celebrated Kleene fixed point theorem is crucial in the mathematical modelling of recursive specifications in Denotational Semantics. In this paperwe discuss whether the hypothesis of the aforementioned result can be weakened. An affirmative answer to the aforesaid inquiry is provided so that a characterization of those properties that a self-mapping must satisfy in order to guarantee that its set of fixed points is non-emptywhen no notion of completeness are assumed to be satisfied by the partially ordered set. Moreover, the case in which the partially ordered set is coming from a quasi-metric space is treated in depth. Finally, an application of the exposed theory is obtained. Concretely, a mathematical method to discuss the asymptotic complexity of those algorithms whose running time of computing fulfills a recurrence equation is presented. Moreover, the aforesaid method retrieves the fixed point basedmethods that appear in the literature for asymptotic complexity analysis of algorithms. However, our new method improves the aforesaid methods because it imposes fewer requirements than those that have been assumed in the literature and, in addition, it allows to state simultaneously upper and lower asymptotic bounds for the running time computing.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-10-01
2019
2019-10-01
2024
2024-09-10
dc.type.none.fl_str_mv research article
http://purl.org/coar/resource_type/c_2df8fbb1
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.12105/22817
url https://hdl.handle.net/20.500.12105/22817
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:Repisalud
instname:Instituto de Salud Carlos III (ISCIII)
instname_str Instituto de Salud Carlos III (ISCIII)
reponame_str Repisalud
collection Repisalud
repository.name.fl_str_mv
repository.mail.fl_str_mv
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