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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
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    Inverse View

    It is not the case that NSPACE(f(n)) ⊆ TIME(2^O(f(n))) for time and space constructible f(n)

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.The proof relies on enumerating all configurations of a nondeterministic machine, but 'configuration' presupposes a fixed, observer-independent notion of machine state.
      ?

      Think about whether this reason is strong or weak

    • 2.Wittgenstein's rule-following considerations show that no finite description uniquely determines its own extension, undermining the assumption that configurations are determinate.
      ?

      Think about whether this reason is strong or weak

    • 3.If configuration-counting is semantically indeterminate, the 2^O(f(n)) bound is not a discovered mathematical fact but a constructed artifact of a chosen formalism.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.The simulation argument assumes that nondeterministic computation is a coherent idealization, but Kripke's skeptical paradox about rule-following applies equally to idealized machine transitions.
      ?

      Think about whether this reason is strong or weak

    • 2.Space constructibility requires that f(n) be computable by a machine that itself presupposes the deterministic-computation framework the theorem is meant to characterize.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.A nondeterministic machine with space bound f(n) can be simulated deterministically in exponential time in f(n)
      ?

      Think about whether this reason is strong or weak

    • 2.f(n) is assumed to be both time and space constructible
      ?

      Think about whether this reason is strong or weak

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    Explore the most compelling reason on the other side.