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    NTIME(t1(n)) is a proper subset of NTIME(t2(n)) when t2(n... — Carmelics
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    NTIME(t1(n)) is a proper subset of NTIME(t2(n)) when t2(n) grows sufficiently faster than t1(n+1)

    All sources support itProof of definition segments
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.t1(n) and t2(n) are time constructible functions
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    • 2.The limit of t1(n+1) / t2(n) as n approaches infinity equals 0
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.The condition 'sufficiently faster' is semantically underspecified absent a formal characterization of the growth rate threshold.
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    • 2.Without a precise boundary condition, the claim functions as a schema rather than a determinate mathematical proposition.
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    • 3.Schemas of this form inherit modal ambiguity that prevents them from serving as proper foundations for complexity-theoretic inference.
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    Reason against 2 of 2
    ?
    • 1.The Nondeterministic Time Hierarchy Theorem requires that t2(n) be fully time-constructible, a condition that is not universally satisfiable for arbitrary growth functions.
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    • 2.If the constructibility requirement fails for edge cases near the growth boundary, the proper subset relation cannot be guaranteed to hold universally.
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    Topics

    Proof of definition segmentsAll sources support it

    Related

    If the constructibility requirement fails for edge cases near the growth boundar...Schemas of this form inherit modal ambiguity that prevents them from serving as ...The Nondeterministic Time Hierarchy Theorem requires that t2(n) be fully time-co...The condition 'sufficiently faster' is semantically underspecified absent a form...
    +3 moreShow less
    The limit of t1(n+1) / t2(n) as n approaches infinity equals 0Without a precise boundary condition, the claim functions as a schema rather tha...t1(n) and t2(n) are time constructible functions

    Similar

    TIME(t1(n)) is a proper subset of TIME(t2(n)) when t2(n) grows suffici...100%NTIME(t1(n)) is a proper subset of NTIME(t2(n)) when t2 grows sufficie...99%TIME(t1(n)) is a proper subset of TIME(t2(n)) when t2 grows sufficient...99%By the Deterministic Time Hierarchy Theorem, if t2(n) grows sufficient...97%

    Source

    AI-extracted1/3 agreementValid
    SEP: computational-complexity
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    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