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The 4^k Barrier for the k-Distinct Language

Theoretical computer science · posed by Ran Ben-Basat, Ariel Gabizon & Meirav Zehavi, 2016 · solved

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Statement

Can the kk-distinct language - words over [n][n] of length at most kk with no repeated symbol - be recognized by an acyclic NFA of size cknO(1)c^k n^{O(1)} for some c<4c < 4? A construction of size 21.96992knO(1)<3.918knO(1)2^{1.96992k} n^{O(1)} < 3.918^k n^{O(1)} answers yes.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    ChatGPT, Codex 5.4-5.6 Pro, Gemini 3.1 Pro

    No person is named on this work: the record names only the tool it came from, and no ProbXiv account is credited for it.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    The gadget-amplification framework - hashing symbols into many copies of a small local NFA gadget - was developed across ChatGPT/Codex 5.4-5.6 Pro and Gemini 3.1 Pro sessions.

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