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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
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    42
    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 grows sufficiently faster than s1

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.The diagonal construction used to separate complexity classes requires that a machine can simulate another within bounded space, but this simulation adds a constant-factor overhead.
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      Think about whether this reason is strong or weak

    • 2.Hartmanis and Stearns' original hierarchy results show that below logarithmic space, the gap conditions for proper separation become insufficient to absorb simulation overhead, meaning the limit condition on s1/s2 alone does not guarantee separation in sub-log regimes.
      ?

      Think about whether this reason is strong or weak

    • 3.Therefore the claim's generality is undermined: sufficiency of the ratio condition is domain-restricted, not universally valid across all space bounds.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Space constructibility presupposes a background computational model, yet the choice of model (Turing machine, RAM, etc.) affects which functions count as constructible.
      ?

      Think about whether this reason is strong or weak

    • 2.If the constructibility criterion is model-relative, the subset relation established by the Space Hierarchy Theorem inherits that relativity and cannot ground a model-independent claim about 'proper' containment.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

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

      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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