English

Correspondences in computational and dynamical complexity II: forcing complex reductions

Computational Complexity 2026-01-16 v1 Dynamical Systems

Abstract

An algebraic telic problem is a decision problem in NPR\textsf{NP}_\mathbb{R} formalizing finite-time reachability questions for one-dimensional dynamical systems. We prove that the existence of "natural" mapping reductions between algebraic telic problems coming from distinct dynamical systems implies the two dynamical systems exhibit similar behavior (in a precise sense). As a consequence, we obtain explicit barriers for algorithms solving algebraic telic problems coming from complex dynamical systems, such as those with positive topological entropy. For example, some telic problems cannot be decided by uniform arithmetic circuit families with only ++ and ×\times gates.

Keywords

Cite

@article{arxiv.2601.09973,
  title  = {Correspondences in computational and dynamical complexity II: forcing complex reductions},
  author = {Samuel Everett},
  journal= {arXiv preprint arXiv:2601.09973},
  year   = {2026}
}

Comments

20 pages, 0 figures

R2 v1 2026-07-01T09:05:07.883Z