A complexity lower bound based on software engineering concepts

Autores
Rojas Paredes, Andrés
Año de publicación
2013
Idioma
español castellano
Tipo de recurso
documento de conferencia
Estado
versión publicada
Descripción
We consider the problem of polynomial equation solving also known as quantifier elimination in Effective Algebraic Geometry. The complexity of the first elimination algorithms were double exponential, but a considerable progress was carried out when the polynomials were represented by arithmetic circuits evaluating them. This representation improves the complexity to pseudo–polynomial time. The question is whether the actual asymptotic complexity of circuit– based elimination algorithms may be improved. The answer is no when elimination algorithms are constructed according to well known software engineering rules, namely applying information hiding and taking into account non–functional requirements. These assumptions allows to prove a complexity lower bound which constitutes a mathematically certified non–functional requirement trade–off and a surprising connection between Software Engineering and the theoretical fields of Algebraic Geometry and Computational Complexity Theory.
WATCC - IV Workshop aspectos teóricos de ciencia de la computación
Red de Universidades con Carreras en Informática (RedUNCI)
Materia
Ciencias Informáticas
non-functional requirement trade–off
information hiding
arithmetic circuit
complexity lower bound
polynomial equation solving
quantifier climination in algebraic geometry
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:10915/32381
Acceder
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spelling A complexity lower bound based on software engineering conceptsRojas Paredes, AndrésCiencias Informáticasnon-functional requirement trade–offinformation hidingarithmetic circuitcomplexity lower boundpolynomial equation solvingquantifier climination in algebraic geometryWe consider the problem of polynomial equation solving also known as quantifier elimination in Effective Algebraic Geometry. The complexity of the first elimination algorithms were double exponential, but a considerable progress was carried out when the polynomials were represented by arithmetic circuits evaluating them. This representation improves the complexity to pseudo–polynomial time. The question is whether the actual asymptotic complexity of circuit– based elimination algorithms may be improved. The answer is no when elimination algorithms are constructed according to well known software engineering rules, namely applying information hiding and taking into account non–functional requirements. These assumptions allows to prove a complexity lower bound which constitutes a mathematically certified non–functional requirement trade–off and a surprising connection between Software Engineering and the theoretical fields of Algebraic Geometry and Computational Complexity Theory.WATCC - IV Workshop aspectos teóricos de ciencia de la computaciónRed de Universidades con Carreras en Informática (RedUNCI)2013-10info:eu-repo/semantics/conferenceObjectinfo:eu-repo/semantics/publishedVersionObjeto de conferenciahttp://purl.org/coar/resource_type/c_5794info:ar-repo/semantics/documentoDeConferenciaapplication/pdfhttp://sedici.unlp.edu.ar/handle/10915/32381spainfo: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:UNLP2025-10-22T16:39:51Zoai:sedici.unlp.edu.ar:10915/32381Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-10-22 16:39:51.89SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv A complexity lower bound based on software engineering concepts
title A complexity lower bound based on software engineering concepts
spellingShingle A complexity lower bound based on software engineering concepts
Rojas Paredes, Andrés
Ciencias Informáticas
non-functional requirement trade–off
information hiding
arithmetic circuit
complexity lower bound
polynomial equation solving
quantifier climination in algebraic geometry
title_short A complexity lower bound based on software engineering concepts
title_full A complexity lower bound based on software engineering concepts
title_fullStr A complexity lower bound based on software engineering concepts
title_full_unstemmed A complexity lower bound based on software engineering concepts
title_sort A complexity lower bound based on software engineering concepts
dc.creator.none.fl_str_mv Rojas Paredes, Andrés
author Rojas Paredes, Andrés
author_facet Rojas Paredes, Andrés
author_role author
dc.subject.none.fl_str_mv Ciencias Informáticas
non-functional requirement trade–off
information hiding
arithmetic circuit
complexity lower bound
polynomial equation solving
quantifier climination in algebraic geometry
topic Ciencias Informáticas
non-functional requirement trade–off
information hiding
arithmetic circuit
complexity lower bound
polynomial equation solving
quantifier climination in algebraic geometry
dc.description.none.fl_txt_mv We consider the problem of polynomial equation solving also known as quantifier elimination in Effective Algebraic Geometry. The complexity of the first elimination algorithms were double exponential, but a considerable progress was carried out when the polynomials were represented by arithmetic circuits evaluating them. This representation improves the complexity to pseudo–polynomial time. The question is whether the actual asymptotic complexity of circuit– based elimination algorithms may be improved. The answer is no when elimination algorithms are constructed according to well known software engineering rules, namely applying information hiding and taking into account non–functional requirements. These assumptions allows to prove a complexity lower bound which constitutes a mathematically certified non–functional requirement trade–off and a surprising connection between Software Engineering and the theoretical fields of Algebraic Geometry and Computational Complexity Theory.
WATCC - IV Workshop aspectos teóricos de ciencia de la computación
Red de Universidades con Carreras en Informática (RedUNCI)
description We consider the problem of polynomial equation solving also known as quantifier elimination in Effective Algebraic Geometry. The complexity of the first elimination algorithms were double exponential, but a considerable progress was carried out when the polynomials were represented by arithmetic circuits evaluating them. This representation improves the complexity to pseudo–polynomial time. The question is whether the actual asymptotic complexity of circuit– based elimination algorithms may be improved. The answer is no when elimination algorithms are constructed according to well known software engineering rules, namely applying information hiding and taking into account non–functional requirements. These assumptions allows to prove a complexity lower bound which constitutes a mathematically certified non–functional requirement trade–off and a surprising connection between Software Engineering and the theoretical fields of Algebraic Geometry and Computational Complexity Theory.
publishDate 2013
dc.date.none.fl_str_mv 2013-10
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info:eu-repo/semantics/publishedVersion
Objeto de conferencia
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dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/32381
url http://sedici.unlp.edu.ar/handle/10915/32381
dc.language.none.fl_str_mv spa
language spa
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
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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
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repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
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