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    SAT is NP-complete. — Carmelics
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    Supports→BHP is in P only if P = NP.

    SAT is NP-complete.

    All sources support itTruth & Knowledge
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.SAT is in NP.
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    • 2.For any X ∈ NP, there exists a non-deterministic Turing machine N accepting X with polynomial time complexity p(n), and all problems in NP are polynomial time reducible to SAT.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Cook's 1971 proof presupposes a fixed computational model (Turing machines), but the notion of 'reduction' is model-relative, not an absolute mathematical fact.
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    • 2.If Church-Turing thesis fails for certain physical or hypercomputational systems, the completeness result loses its claimed universality across all possible computation.
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    Reason against 2 of 2
    ?
    • 1.NP-completeness proofs rely on an encoding of problem instances as strings, but the choice of encoding is conventional and can alter polynomial-time reducibility relations.
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    • 2.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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    Topics

    Truth & KnowledgeAll sources support it

    Connections

    1 linked claim · 1 topic

    Modality & Possibility3 linked
    BHP is in P only if P = NP.

    Related

    Cook's 1971 proof presupposes a fixed computational model (Turing machines), but...For any X ∈ NP, there exists a non-deterministic Turing machine N accepting X wi...If Church-Turing thesis fails for certain physical or hypercomputational systems...NP-completeness proofs rely on an encoding of problem instances as strings, but ...
    +2 moreShow less
    SAT is in NP.Since the claim 'SAT is NP-complete' is only provably true relative to a chosen ...

    Similar

    TQBF is PSPACE-complete.100%BHP is NP-complete.100%TWO PLAYER SAT is PSPACE-complete.98%TQBF is PSPACE-complete98%

    Source

    AI-extracted1/3 agreementValid
    SEP: computational-complexity
    View source passageHide passage
    For instance, the following is often described as the single most important open question in all of theoretical computer science: Open Question 1 Is \(\textbf{P}\) properly contained in \(\textbf{NP}\)? 1. 3 Reductions and \(\textbf{NP}\)-completeness Having now introduced some of the major classes studied in complexity theory, we next turn to the question of their internal structure. This can be studied using the notions of the reducibility of one problem to another and of a problem being comp
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit