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    Since the claim 'SAT is NP-complete' is only provably tru... — Carmelics
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    Part of a larger discussion

    Challenges→SAT is NP-complete.

    Since the claim 'SAT is NP-complete' is only provably true relative to a chosen encoding scheme, it is a representational artifact rather than an intrinsic mathematical truth about satisfiability.

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    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.NP-completeness proofs require encoding problems as strings; changing the encoding scheme can change which problems are in NP.
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    • 2.Mathematical truths about abstract satisfiability (solvability) exist independently of any particular symbol system or representation.
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    • 3.If the same abstract problem yields different complexity classes under different encodings, the complexity property depends on representation, not the problem itself.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Standard polynomial-time encodings (binary, decimal) all yield the same complexity classes due to logarithmic inter-reducibility between them.
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    • 2.NP-completeness is defined relative to the standard computational model; 'reasonable encoding' is built into the definition, not an arbitrary choice.
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    • 3.Saying results depend on encoding confuses the model of computation with the mathematical structure; the intrinsic property is model-relative from the start.
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    Key Terms

    Encoding scheme(in philosophy of mathematics and representation)
    A system or method for representing information or data, like how we might write numbers in binary versus decimal.
    Intrinsic mathematical truth(as used in philosophy of mathematics and metaphysics)
    A fact about math that is true on its own, independent of how we write it down or what symbols we use—something genuinely true about the subject itself.
    NP-complete(Complexity theory classification of hardest problems within NP.)
    A problem is NP-complete if it is in NP and every problem in NP is polynomial-time reducible to it, making it among the most difficult problems in NP.
    Representational artifact(as used in philosophy of physics and epistemology)
    Something that appears to be a real problem or flaw, but is actually just a quirk of how we're describing or representing the situation—not a genuine issue with reality itself.
    SAT (Boolean satisfiability problem)(in computational logic)
    A famous computer science problem that asks: can you assign true or false values to variables in a logical formula to make the whole thing true?
    satisfiability(classical first-order logic)
    A formula φ of language L is satisfiable if and only if there exists a Σ-structure A and assignment s on it such that A,s⊨φ holds.

    Connections

    1 linked claim · 2 topics

    All sources support it1 linkedTruth & Knowledge1 linked
    SAT is NP-complete.

    Related

    If the same abstract problem yields different complexity classes under different...

    Details

    Type
    claim
    Perspectives
    2 (1 for, 1 against)
    Edits
    1 edit
    Mathematical truths about abstract satisfiability (solvability) exist independen...
    NP-completeness is defined relative to the standard computational model; 'reason...
    NP-completeness proofs require encoding problems as strings; changing the encodi...
    +3 moreShow less
    SAT is NP-complete.Saying results depend on encoding confuses the model of computation with the mat...Standard polynomial-time encodings (binary, decimal) all yield the same complexi...