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Probabilistic Automatic Complexity Is At Most Three

Theoretical computer science · posed by Christopher Gill, 2024 · solved

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Statement

Gill introduced the probabilistic automatic complexity AP(w)A_P(w) of a string: the least number of states of a probabilistic finite automaton for which ww is the unique most probably accepted string of its length. He asked whether APA_P is unbounded, no string with AP>3A_P>3 being known. The paper proves AP(w)≤3A_P(w)\le 3 for every string over every finite alphabet, with an explicit three-state witness.

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

  1. construction · #1

    Bjørn Kjos-Hanssen, using Claude Fable 5

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

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

    The author states the construction was found in conversation with, and verified with the assistance of, Claude Fable 5, and that the proof was formalized in Lean with assistance from Harmonic's Aristotle.

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