The Real Dimension Problem Is Np R -complete Ecole Normale Supérieure De Lyon the Real Dimension Problem Is Np R -complete R Esum E the Real Dimension Problem Is Np R -complete
نویسنده
چکیده
We show that computing the dimension of a semi-algebraic set of R n is a NP R-complete problem in the Blum-Shub-Smale model of computation over the reals. Since this problem is easily seen to be NP R-hard, the main ingredient of the proof is a NP R algorithm for computing the dimension. On montre que le calcul de la dimension d'un ensemble semi-alg ebrique de R n est un probl eme NP R-complet dans le mod ele de Blum-Shub-Smale de calcul sur les nombres r eels. Puisqu'il est facile de voir que ce probl eme est NP R-dur, le principal ingr edient de la preuve est un algorithme NP R de calcul de la dimension. Abstract We show that computing the dimension of a semi-algebraic set of R n is a NP R-complete problem in the Blum-Shub-Smale model of computation over the reals. Since this problem is easily seen to be NP R-hard, the main ingredient of the proof is a NP R algorithm for computing the dimension.
منابع مشابه
The Real Dimension Problem
We show that computing the dimension of a semi-algebraic set of R n is a NP R-complete problem in the Blum-Shub-Smale model of computation over the reals. Since this problem is easily seen to be NP R-hard, the main ingredient of the proof is a NP R algorithm for computing the dimension.
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