Description of the connected components of a semialgebraic set in single exponential time

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This paper is devoted to the following result: let R be a real closed field and let S be a semialgebraic subset of Rn defined by a boolean combination of polynomial inequalities. Let D be the sum of the degrees of the polynomials involved. Then it is possible to find algorithmically a description of...

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Autores principales: Heintz, J., Roy, M.-F., Solernó, P.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_01795376_v11_n1_p121_Heintz
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_01795376_v11_n1_p121_Heintz2023-10-03T15:08:31Z Description of the connected components of a semialgebraic set in single exponential time Heintz, J. Roy, M.-F. Solernó, P. This paper is devoted to the following result: let R be a real closed field and let S be a semialgebraic subset of Rn defined by a boolean combination of polynomial inequalities. Let D be the sum of the degrees of the polynomials involved. Then it is possible to find algorithmically a description of the semialgebraically connected components of S in sequential time Dn o(1) and parallel time (n log D)o(1) This implies that the problem of finding the connected components of a semialgebraic set can be solved in P-SPACE. © 1994 Springer-Verlag New York Inc. Fil:Solernó, P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_01795376_v11_n1_p121_Heintz
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description This paper is devoted to the following result: let R be a real closed field and let S be a semialgebraic subset of Rn defined by a boolean combination of polynomial inequalities. Let D be the sum of the degrees of the polynomials involved. Then it is possible to find algorithmically a description of the semialgebraically connected components of S in sequential time Dn o(1) and parallel time (n log D)o(1) This implies that the problem of finding the connected components of a semialgebraic set can be solved in P-SPACE. © 1994 Springer-Verlag New York Inc.
format JOUR
author Heintz, J.
Roy, M.-F.
Solernó, P.
spellingShingle Heintz, J.
Roy, M.-F.
Solernó, P.
Description of the connected components of a semialgebraic set in single exponential time
author_facet Heintz, J.
Roy, M.-F.
Solernó, P.
author_sort Heintz, J.
title Description of the connected components of a semialgebraic set in single exponential time
title_short Description of the connected components of a semialgebraic set in single exponential time
title_full Description of the connected components of a semialgebraic set in single exponential time
title_fullStr Description of the connected components of a semialgebraic set in single exponential time
title_full_unstemmed Description of the connected components of a semialgebraic set in single exponential time
title_sort description of the connected components of a semialgebraic set in single exponential time
url http://hdl.handle.net/20.500.12110/paper_01795376_v11_n1_p121_Heintz
work_keys_str_mv AT heintzj descriptionoftheconnectedcomponentsofasemialgebraicsetinsingleexponentialtime
AT roymf descriptionoftheconnectedcomponentsofasemialgebraicsetinsingleexponentialtime
AT solernop descriptionoftheconnectedcomponentsofasemialgebraicsetinsingleexponentialtime
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