English

Explaining the Ubiquity of Phase Transitions in Decision Problems

Computational Complexity 2025-01-27 v1

Abstract

I present an analytic approach to establishing the presence of phase transitions in a large set of decision problems. This approach does not require extensive computational study of the problems considered. The set -- that of all paddable problems over even-sized alphabets satisfying a condition similar to not being sparse -- shown to exhibit phase transitions contains many "practical" decision problems, is very large, and also contains extremely intractable problems.

Keywords

Cite

@article{arxiv.2501.14569,
  title  = {Explaining the Ubiquity of Phase Transitions in Decision Problems},
  author = {Andrew Jackson},
  journal= {arXiv preprint arXiv:2501.14569},
  year   = {2025}
}
R2 v1 2026-06-28T21:16:22.792Z