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.
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}
}