Le problème Des granDes puissances et celui Des granDes racines

Journal of Symbolic Logic 65 (4):1675-1685 (2000)
  Copy   BIBTEX

Abstract

Let f be a function from N to N that can not be computed in polynomial time, and let a be an element of a differential field K of characteristic 0. The problem of large powers is the set of tuples x̄ = (x 1 ,..., x n ) of K so that x 1 = a f(n) , and the problem of large roots is the set of tuples x̄ of K so that x f(n) 1 = a. These are two examples of problems that the use of derivation does not allow to solve quicker. We show that the problem of large roots is not polynomial for the differential field K, even if we use a polynomial number of parameters, and that the problem of large powers is not polynomial for the differential field K, even for non-uniform complexity. The proofs use the polynomial stability (i.e., the elimination of parameters) of field of characteristic 0, shown by L. Blum. F. Cucker. M. Shub and S. Smale, and the reduction lemma, that transforms a differential polynomial in variables x̄ into a polynomial in variables x̄. and their derivatives

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 74,213

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Analytics

Added to PP
2009-01-28

Downloads
14 (#724,806)

6 months
1 (#414,449)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references