Linearizing well quasi-orders and bounding the length of bad sequences

Autores
Abriola, Sergio Alejandro; Figueira, Santiago; Senno, Gabriel Ignacio
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the length functions of controlled bad sequences over some well quasi-orders (wqo's) and classify them in the Fast Growing Hierarchy. We develop a new and self-contained study of the length of bad sequences over the disjoint product in Nn (Dickson's Lemma), which leads to recently discovered upper bounds but through a simpler argument. We also give a tight upper bound for the length of controlled decreasing sequences of multisets of Nn with the underlying lexicographic ordering, and use it to give an upper bound for the length of controlled bad sequences in the majoring ordering with the underlying disjoint product ordering. We apply this last result to attain complexity upper bounds for the emptiness problem of itca and atra automata. For the case of the product and majoring wqo's the idea is to linearize bad sequences, i.e. to transform a bad sequence over a wqo into a decreasing one over a well-order, for which upper bounds can be more easily handled.
Fil: Abriola, Sergio Alejandro. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Figueira, Santiago. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Senno, Gabriel Ignacio. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Controlled Bad Sequence
Fast Growing Hierarchy
Lexicographic Ordering
Majoring Ordering
Multiset Ordering
Product Ordering
Well Quasi-Order
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/59573
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/59573
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Linearizing well quasi-orders and bounding the length of bad sequencesAbriola, Sergio AlejandroFigueira, SantiagoSenno, Gabriel IgnacioControlled Bad SequenceFast Growing HierarchyLexicographic OrderingMajoring OrderingMultiset OrderingProduct OrderingWell Quasi-Orderhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the length functions of controlled bad sequences over some well quasi-orders (wqo's) and classify them in the Fast Growing Hierarchy. We develop a new and self-contained study of the length of bad sequences over the disjoint product in Nn (Dickson's Lemma), which leads to recently discovered upper bounds but through a simpler argument. We also give a tight upper bound for the length of controlled decreasing sequences of multisets of Nn with the underlying lexicographic ordering, and use it to give an upper bound for the length of controlled bad sequences in the majoring ordering with the underlying disjoint product ordering. We apply this last result to attain complexity upper bounds for the emptiness problem of itca and atra automata. For the case of the product and majoring wqo's the idea is to linearize bad sequences, i.e. to transform a bad sequence over a wqo into a decreasing one over a well-order, for which upper bounds can be more easily handled.Fil: Abriola, Sergio Alejandro. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Figueira, Santiago. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Senno, Gabriel Ignacio. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaElsevier Science2015-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/59573Abriola, Sergio Alejandro; Figueira, Santiago; Senno, Gabriel Ignacio; Linearizing well quasi-orders and bounding the length of bad sequences; Elsevier Science; Theoretical Computer Science; 603; 10-2015; 3-220304-3975CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0304397515006337info:eu-repo/semantics/altIdentifier/doi/10.1016/j.tcs.2015.07.012info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:59:56Zoai:ri.conicet.gov.ar:11336/59573instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:59:56.825CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Linearizing well quasi-orders and bounding the length of bad sequences
title Linearizing well quasi-orders and bounding the length of bad sequences
spellingShingle Linearizing well quasi-orders and bounding the length of bad sequences
Abriola, Sergio Alejandro
Controlled Bad Sequence
Fast Growing Hierarchy
Lexicographic Ordering
Majoring Ordering
Multiset Ordering
Product Ordering
Well Quasi-Order
title_short Linearizing well quasi-orders and bounding the length of bad sequences
title_full Linearizing well quasi-orders and bounding the length of bad sequences
title_fullStr Linearizing well quasi-orders and bounding the length of bad sequences
title_full_unstemmed Linearizing well quasi-orders and bounding the length of bad sequences
title_sort Linearizing well quasi-orders and bounding the length of bad sequences
dc.creator.none.fl_str_mv Abriola, Sergio Alejandro
Figueira, Santiago
Senno, Gabriel Ignacio
author Abriola, Sergio Alejandro
author_facet Abriola, Sergio Alejandro
Figueira, Santiago
Senno, Gabriel Ignacio
author_role author
author2 Figueira, Santiago
Senno, Gabriel Ignacio
author2_role author
author
dc.subject.none.fl_str_mv Controlled Bad Sequence
Fast Growing Hierarchy
Lexicographic Ordering
Majoring Ordering
Multiset Ordering
Product Ordering
Well Quasi-Order
topic Controlled Bad Sequence
Fast Growing Hierarchy
Lexicographic Ordering
Majoring Ordering
Multiset Ordering
Product Ordering
Well Quasi-Order
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We study the length functions of controlled bad sequences over some well quasi-orders (wqo's) and classify them in the Fast Growing Hierarchy. We develop a new and self-contained study of the length of bad sequences over the disjoint product in Nn (Dickson's Lemma), which leads to recently discovered upper bounds but through a simpler argument. We also give a tight upper bound for the length of controlled decreasing sequences of multisets of Nn with the underlying lexicographic ordering, and use it to give an upper bound for the length of controlled bad sequences in the majoring ordering with the underlying disjoint product ordering. We apply this last result to attain complexity upper bounds for the emptiness problem of itca and atra automata. For the case of the product and majoring wqo's the idea is to linearize bad sequences, i.e. to transform a bad sequence over a wqo into a decreasing one over a well-order, for which upper bounds can be more easily handled.
Fil: Abriola, Sergio Alejandro. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Figueira, Santiago. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Senno, Gabriel Ignacio. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We study the length functions of controlled bad sequences over some well quasi-orders (wqo's) and classify them in the Fast Growing Hierarchy. We develop a new and self-contained study of the length of bad sequences over the disjoint product in Nn (Dickson's Lemma), which leads to recently discovered upper bounds but through a simpler argument. We also give a tight upper bound for the length of controlled decreasing sequences of multisets of Nn with the underlying lexicographic ordering, and use it to give an upper bound for the length of controlled bad sequences in the majoring ordering with the underlying disjoint product ordering. We apply this last result to attain complexity upper bounds for the emptiness problem of itca and atra automata. For the case of the product and majoring wqo's the idea is to linearize bad sequences, i.e. to transform a bad sequence over a wqo into a decreasing one over a well-order, for which upper bounds can be more easily handled.
publishDate 2015
dc.date.none.fl_str_mv 2015-10
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/59573
Abriola, Sergio Alejandro; Figueira, Santiago; Senno, Gabriel Ignacio; Linearizing well quasi-orders and bounding the length of bad sequences; Elsevier Science; Theoretical Computer Science; 603; 10-2015; 3-22
0304-3975
CONICET Digital
CONICET
url http://hdl.handle.net/11336/59573
identifier_str_mv Abriola, Sergio Alejandro; Figueira, Santiago; Senno, Gabriel Ignacio; Linearizing well quasi-orders and bounding the length of bad sequences; Elsevier Science; Theoretical Computer Science; 603; 10-2015; 3-22
0304-3975
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0304397515006337
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.tcs.2015.07.012
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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