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    Complexity classifications are encoding-relative, so clai... — Carmelics
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    Challenges→BHP is NP-complete

    Complexity classifications are encoding-relative, so claiming BHP is NP-complete without specifying the encoding is a category error, not a theorem (cf. Papadimitriou 1994).

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    Reasons For

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    • 1.Unary vs binary encoding can shift BHP from polynomial to exponential time, making complexity claims encoding-dependent per Papadimitriou.
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    • 2.Standard complexity theory requires implicit encoding assumptions; stating them explicitly avoids conflating formal results with domain-independent claims.
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    • 3.Calling something 'NP-complete' without encoding specification risks semantic ambiguity equivalent to claiming theorems without specifying axiom systems.
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    Reasons Against

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    • 1.The complexity community has stable conventions (binary encoding default) making encoding specification a pragmatic norm, not a logical requirement.
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    • 2.Encoding-relativism doesn't invalidate BHP's NP-completeness status—it clarifies a technical parameter, not a category error in mathematical theoremhood.
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    • 3.Requiring explicit encoding for every complexity claim would paralyze discourse; we don't call Peano axioms 'not theorems' for requiring arithmetic assumptions.
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    BHP is NP-complete

    Related

    BHP is NP-completeCalling something 'NP-complete' without encoding specification risks semantic am...Encoding-relativism doesn't invalidate BHP's NP-completeness status—it clarifies...Requiring explicit encoding for every complexity claim would paralyze discourse;...
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    Standard complexity theory requires implicit encoding assumptions; stating them ...The complexity community has stable conventions (binary encoding default) making...Unary vs binary encoding can shift BHP from polynomial to exponential time, maki...

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