David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 65 (4):1675-1685 (2000)
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
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Uwe Egly & Hans Tompits (2003). On Different Proof-Search Strategies for Orthologic. Studia Logica 73 (1):131 - 152.
Andreas Blass, Yuri Gurevich & Saharon Shelah (2002). On Polynomial Time Computation Over Unordered Structures. Journal of Symbolic Logic 67 (3):1093-1125.
Stephen A. Fenner, Stuart A. Kurtz & James S. Royer (2004). Every Polynomial-Time 1-Degree Collapses If and Only If P = Pspace. Journal of Symbolic Logic 69 (3):713-741.
F. Tudoret, A. Bardou & G. Carrault (2001). Numerically Solving Physiological Models Based on a Polynomial Approach. Acta Biotheoretica 49 (4):247-260.
Erik Aarts (1994). Proving Theorems of the Second Order Lambek Calculus in Polynomial Time. Studia Logica 53 (3):373 - 387.
Douglas Cenzer & Jeffrey B. Remmel (2006). Complexity, Decidability and Completeness. Journal of Symbolic Logic 71 (2):399 - 424.
Alexis Bès (2000). An Extension of the Cobham-Semënov Theorem. Journal of Symbolic Logic 65 (1):201-211.
Arnold Beckmann & Samuel R. Buss (2009). Polynomial Local Search in the Polynomial Hierarchy and Witnessing in Fragments of Bounded Arithmetic. Journal of Mathematical Logic 9 (01):103-138.
Thomas Strahm (1997). Polynomial Time Operations in Explicit Mathematics. Journal of Symbolic Logic 62 (2):575-594.
Natacha Portier (1999). Stabilité Polynômiale Des Corps Différentiels. Journal of Symbolic Logic 64 (2):803-816.
Added to index2009-01-28
Total downloads2 ( #511,927 of 1,699,833 )
Recent downloads (6 months)2 ( #269,935 of 1,699,833 )
How can I increase my downloads?