Generalisation of Baker's Forcing Method to Arbitrary Prime and NP-hardness of Several $p$-adic Optimisations

Tomoki Mihara

Generalisation of Baker's Forcing Method to Arbitrary Prime and NP-hardness of Several $p$-adic Optimisations

Computational Complexity 2026-07-07 v1 Number Theory

Authors: Tomoki Mihara

Abstract

G.\ D.\ Baker formulated a forcing method to interpret integer optimisation problem into $2$ -adic linear regression, and proved the NP-hardness of $2$ -adic linear regression. We generalise the forcing method to a wider class of $p$ -adic optimisation for the case where $p$ is not necessarily $2$ , and prove the NP-hardness of $p$ -adic linear regression, the NP-hardness of $2$ -adic dynamic neural network by S.\ Albeverio, A.\ Khrennikov, and B.\ Tirrozi, and the NP-hardness of a partial generalisation of the $p$ -adic optimisation problem associated to van der Put neural network by G.\ L.\ R.\ N'guessan.

Keywords

p-adic optimization NP-hardness forcing method linear regression neural networks computational complexity

Cite

@article{arxiv.2607.06092,
  title  = {Generalisation of Baker's Forcing Method to Arbitrary Prime and NP-hardness of Several $p$-adic Optimisations},
  author = {Tomoki Mihara},
  journal= {arXiv preprint arXiv:2607.06092},
  year   = {2026}
}