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Explaining the Ubiquity of Phase Transitions in Decision Problems

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arxiv 2501.14569 v1 pith:2ERWS4NV submitted 2025-01-24 cs.CC

Andrew Jackson This is my paper · ORCID
classification cs.CC
keywords problemsdecisionphasetransitionsapproachcontainslargealphabets
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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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  1. Phase Transitions in Decision Problems Over Odd-Sized Alphabets

    cs.CC 2025-05 reject novelty 4.0 of 10

    A follow-up theorem claims phase transitions appear in all adequately-balanced decision problems over odd-sized alphabets, but the proof's central alphabet-encoding construction is invalid as written.

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