Scheme-theoretic Approach to Computational Complexity II. The Separation of P and NP over $\mathbb{C}$, $\mathbb{R}$, and $\mathbb{Z}$
Computational Complexity
2024-02-23 v9
Abstract
We show that the problem of determining the feasibility of quadratic systems over , , and requires exponential time. This separates P and NP over these fields/rings in the BCSS model of computation.
Keywords
Cite
@article{arxiv.2107.07387,
title = {Scheme-theoretic Approach to Computational Complexity II. The Separation of P and NP over $\mathbb{C}$, $\mathbb{R}$, and $\mathbb{Z}$},
author = {Ali Çivril},
journal= {arXiv preprint arXiv:2107.07387},
year = {2024}
}
Comments
4 pages, updated the definitions according to the first paper in the series