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    Home/Original/inverse
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    Inverse View

    It is not the case that NTIME(t1(n)) is a proper subset of NTIME(t2(n)) when t2(n) grows sufficiently faster than t1(n+1)

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 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 for 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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    Reasons Against

    1 perspective
    Reason against
    ?
    • 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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