The Lagrangian remainder of Taylor's series, distinguishes O(f(x)) time complexities to polynomials or not

2020/01/30 by Bakas, Nikolaos P., Kosmatopoulos, Elias, Nicolaou, Mihalis +1
#Computational Complexity (cs.CC) #FOS: Computer and information sciences

paper · doi:10.48550/arxiv.2001.11811

Abstract

The purpose of this letter is to investigate the time complexity consequences of the truncated Taylor series, known as Taylor Polynomials \citebakas2019taylor,Katsoprinakis2011,Nestoridis2011. In particular, it is demonstrated that the examination of the P=NP equality, is associated with the determination of whether the n^th derivative of a particular solution is bounded or not. Accordingly, in some cases, this is not true, and hence in general.

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