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    Constructing a truth table is exponential in the number o... — Carmelics
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    Part of a larger discussion

    Challenges→If P = NP, then finding a satisfying valuation for a propositional formula would be no harder than constructing its truth table

    Constructing a truth table is exponential in the number of variables, not polynomial, so it cannot serve as the baseline for 'no harder than'.

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    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Exponential algorithms (2^n) are fundamentally distinct from polynomial ones in computational complexity theory and practice.
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    • 2.Using an exponential-time procedure as a baseline allows intractable problems to appear tractable by comparison.
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    • 3.For complexity comparisons to be meaningful, the reference point must itself be efficiently computable.
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    Reasons Against

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    Reason against
    ?
    • 1.Truth tables directly encode logical equivalence; their exponential size reflects the problem's inherent information content, not measurement error.
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    • 2.Comparison is meaningful even between intractable methods; we can still say algorithm A is 'no harder than' algorithm B if A's complexity ≤ B's.
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    • 3.Restricting baselines to polynomial algorithms begs the question by assuming only polynomial bounds count as legitimate reference points.
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    Connections

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    Proof of definition segments1 linkedTruth & Knowledge1 linked

    Related

    Comparison is meaningful even between intractable methods; we can still say algo...Exponential algorithms (2^n) are fundamentally distinct from polynomial ones in ...For complexity comparisons to be meaningful, the reference point must itself be ...If P = NP, then finding a satisfying valuation for a propositional formula would...
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    Restricting baselines to polynomial algorithms begs the question by assuming onl...Truth tables directly encode logical equivalence; their exponential size reflect...Using an exponential-time procedure as a baseline allows intractable problems to...

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    claim
    Perspectives
    2 (1 for, 1 against)
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