Scheme-theoretic Approach to Computational Complexity II. The Separation of P and NP over $\mathbb{C}$, $\mathbb{R}$, and $\mathbb{Z}$

Ali Çivril

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arXiv · 2107.07387

Scheme-theoretic Approach to Computational Complexity II. The Separation of P and NP over $\mathbb{C}$, $\mathbb{R}$, and $\mathbb{Z}$

Ali Çivril

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Abstract

We show that the problem of determining the feasibility of quadratic systems over $\mathbb{C}$, $\mathbb{R}$, and $\mathbb{Z}$ requires exponential time. This separates P and NP over these fields/rings in the BCSS model of computation.

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Ali Çivril. 2021-07-06. Scheme-theoretic Approach to Computational Complexity II. The Separation of P and NP over $\mathbb{C}$, $\mathbb{R}$, and $\mathbb{Z}$. https://arxiv.org/abs/2107.07387

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