English

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 C\mathbb{C}, R\mathbb{R}, and Z\mathbb{Z} 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