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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
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    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that The space hierarchy theorem's proof relies on a diagonalization argument that presupposes a universal TM can simulate any TM with bounded overhead.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.The 'bounded overhead' claim conflates worst-case and average-case complexity; overhead varies by TM structure.
      ?

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    • 2.Space hierarchy's proof doesn't strictly require bounded simulation—relative separation suffices without tight overhead bounds.
      ?

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    • 3.Presupposing bounded overhead risks circularity: we assume what space hierarchy aims to establish about resource separability.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Universal TMs can simulate any TM; this is Church-Turing thesis, foundational to computability theory.
      ?

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    • 2.The overhead is bounded by a constant factor plus logarithmic terms; proven constructively in standard references.
      ?

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    • 3.Diagonalization requires this simulation property to construct a TM exceeding any resource bound, making the argument valid.
      ?

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