Scheme-theoretic Approach to Computational Complexity I. The Separation of P and NP
Computational Complexity
2024-02-20 v9
Abstract
We lay the foundations of a new theory for algorithms and computational complexity by parameterizing the instances of a computational problem as a moduli scheme. Considering the geometry of the scheme associated to 3-SAT, we separate P and NP. In particular, we show that no deterministic algorithm can solve \textsf{3-SAT} in time less than in the worst case.
Cite
@article{arxiv.2107.07386,
title = {Scheme-theoretic Approach to Computational Complexity I. The Separation of P and NP},
author = {Ali Çivril},
journal= {arXiv preprint arXiv:2107.07386},
year = {2024}
}
Comments
15 pages, more formal definitions unit reductions, proof (of the almost obvious fact) that unit operations are distinct from unit instance operations