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    Haken's 1985 proof relies on a specific syntactic formali... — Carmelics
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    Challenges→Resolution is not polynomially bounded.

    Haken's 1985 proof relies on a specific syntactic formalization of PHP_n; alternative encodings may yield structurally distinct tautologies with shorter proofs.

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    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Proof length depends on syntactic choices: different variable orderings and clause representations demonstrably affect resolution proof size.
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    • 2.PHP has multiple logically equivalent formalizations; some encodings may distribute the pigeonhole constraint more efficiently than others.
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    • 3.Haken's lower bound applies to *specific* proof systems and encodings, not to all possible representations of the same logical content.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Haken's exponential lower bound applies to the *formula class* PHP_n itself, not just one syntactic instance—alternative encodings are equivalent.
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    • 2.No alternative encoding has demonstrated substantially shorter proofs in practice; marginal syntactic improvements don't overcome the fundamental barrier.
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    • 3.The claim conflates encoding variations (which exist) with proof-theoretic hardness (which is invariant across reasonable formalizations).
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    Related

    Haken's exponential lower bound applies to the *formula class* PHP_n itself, not...Haken's lower bound applies to *specific* proof systems and encodings, not to al...No alternative encoding has demonstrated substantially shorter proofs in practic...PHP has multiple logically equivalent formalizations; some encodings may distrib...
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    Proof length depends on syntactic choices: different variable orderings and clau...Resolution is not polynomially bounded.The claim conflates encoding variations (which exist) with proof-theoretic hardn...

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    claim
    Perspectives
    2 (1 for, 1 against)
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    1 edit