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    P is a subset of NP — Carmelics
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    Home/Modality & Possibility
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    P is a subset of NP

    Modality & PossibilityTruth & 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
    ?
    • Every deterministic Turing machine is by definition a non-deterministic machine
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.The inclusion P⊆NP is trivially true by definition, making it philosophically uninformative about computational tractability.
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    • 2.The substantive open question—whether P=NP or P≠NP—cannot be resolved by definitional containment alone.
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    • 3.Conflating the trivial set-theoretic inclusion with the deep complexity-theoretic question equivocates on the epistemic weight of the claim.
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    Reason against 2 of 2
    ?
    • 1.Baker, Gill, and Solovay (1975) demonstrated that relativized proofs cannot settle P vs NP, suggesting the question resists standard formal methods.
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    • 2.If standard proof techniques are systematically inadequate, the claim P⊆NP—while technically true—may obscure an unprovable or independent proposition about P=NP.
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    • 3.Gödel's incompleteness results establish precedent for mathematically well-formed questions that are formally undecidable within standard axiom systems.
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    Related

    Baker, Gill, and Solovay (1975) demonstrated that relativized proofs cannot sett...Conflating the trivial set-theoretic inclusion with the deep complexity-theoreti...Every deterministic Turing machine is by definition a non-deterministic machineGödel's incompleteness results establish precedent for mathematically well-forme...
    +3 moreShow less
    If standard proof techniques are systematically inadequate, the claim P⊆NP—while...The inclusion P⊆NP is trivially true by definition, making it philosophically un...The substantive open question—whether P=NP or P≠NP—cannot be resolved by definit...

    Similar

    PSPACE is a subset of NPSPACE100%P is a subset of BPP100%NC is a subset of P100%PSPACE is a subset of NPSPACE (PSPACE ⊆ NPSPACE)96%

    Source

    AI-extracted1/3 agreementValid
    SEP: computational-complexity
    View source passageHide passage
    2 Complexity classes and the hierarchy theorems Recall that a complexity class is a set of languages all of which can be decided within a given time or space complexity bound \(t(n)\) or \(s(n)\) with respect to a fixed model of computation. g. non-recursive ones) it is standard to restrict attention to complexity classes defined when \(t(n)\) and \(s(n)\) are time or space constructible. e. a string of \(n\) 1s) halts after exactly \(t(n)\) steps. Similarly, \(s(n)\) is said to be space constru
    Extraction notes

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

    Details

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