Explaining the Ubiquity of Phase Transitions in Decision Problems

TL;DR

This paper introduces an analytical method to identify phase transitions in a broad class of decision problems, including practical and intractable cases, without extensive computational analysis.

Contribution

It provides a novel analytic framework to establish phase transitions in decision problems, expanding understanding beyond computational experiments.

Findings

Large set of decision problems exhibit phase transitions

Method applies to practical and intractable problems

No extensive computation needed for analysis

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.