Explaining the Ubiquity of Phase Transitions in Decision Problems

Andrew Jackson

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arXiv · 2501.14569

Explaining the Ubiquity of Phase Transitions in Decision Problems

Andrew Jackson

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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.

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Andrew Jackson. 2025-01-24. Explaining the Ubiquity of Phase Transitions in Decision Problems. https://arxiv.org/abs/2501.14569

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