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    Cook and Reckhow's framework conflates proof length with ... — Carmelics
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    Challenges→The system P_1 admits proofs of PHP_n of size polynomial in n.

    Cook and Reckhow's framework conflates proof length with proof comprehensibility, obscuring that short formal derivations may require exponential search to discover.

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    Reasons For

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    Reason for
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    • 1.A proof's length measures output complexity, not the computational difficulty of finding it during derivation search.
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    • 2.SAT solvers often discover exponentially-long execution paths to reach short proofs, indicating search cost ≠ proof length.
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    • 3.Comprehensibility requires understanding how to derive a result, which demands knowledge of the search process, not just final form.
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    Reasons Against

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    • 1.Cook-Reckhow defines proof systems formally by verification polynomial-time, not discovability; conflation claim misrepresents their framework.
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    • 2.Proof comprehensibility is about readable structure and logical clarity, which short proofs often provide better than long ones.
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    • 3.Distinguishing search hardness from proof length is valuable but doesn't invalidate using proof length as a complexity measure.
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    Truth & Knowledge1 linkedModality & Possibility1 linked

    Related

    A proof's length measures output complexity, not the computational difficulty of...Comprehensibility requires understanding how to derive a result, which demands k...Cook-Reckhow defines proof systems formally by verification polynomial-time, not...Distinguishing search hardness from proof length is valuable but doesn't invalid...
    +3 moreShow less
    Proof comprehensibility is about readable structure and logical clarity, which s...SAT solvers often discover exponentially-long execution paths to reach short pro...The system P_1 admits proofs of PHP_n of size polynomial in n.

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