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
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/32381
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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:UNLP2025-09-29T10:58:20Zoai: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:13292025-09-29 10:58:20.547SEDICI (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 |
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 |
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conferenceObject |
status_str |
publishedVersion |
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http://sedici.unlp.edu.ar/handle/10915/32381 |
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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 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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SEDICI (UNLP) - Universidad Nacional de La Plata |
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