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    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that SPACE(s1(n)) is a proper subset of SPACE(s2(n)) when s2(n) grows sufficiently faster than s1(n)

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.The space hierarchy theorem's proof relies on a diagonalization argument that presupposes a universal TM can simulate any TM with bounded overhead.
      ?

      Think about whether this reason is strong or weak

    • 2.The simulation overhead assumption embeds a non-trivial empirical claim about machine architecture that is not derivable from pure mathematical definitions of SPACE classes.
      ?

      Think about whether this reason is strong or weak

    • 3.If the overhead of universal simulation is not tightly bounded, the strict separation between SPACE(s1(n)) and SPACE(s2(n)) may not hold for all constructible function pairs satisfying the ratio condition.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Space constructibility is a non-trivial precondition: not all mathematically well-defined functions s(n) >= n are space constructible in the required sense.
      ?

      Think about whether this reason is strong or weak

    • 2.The claim's scope is implicitly restricted to a proper subset of function pairs, making the theorem's generality philosophically overstated when presented without that qualification.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.s1(n) and s2(n) are space constructible functions with s2(n) >= s1(n) >= n
      ?

      Think about whether this reason is strong or weak

    • 2.The limit of s1(n) / s2(n) as n approaches infinity equals 0
      ?

      Think about whether this reason is strong or weak

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