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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 P is a proper subset of TIME(f(n)) for any super-polynomial time bound f(n)

    ?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 Time Hierarchy Theorem assumes a specific computational model (multi-tape TM), and model-relativity means containment claims may not transfer across equivalent formalisms.
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    • 2.Philosophical accounts of mathematical truth (e.g., Benacerraf, Field) distinguish provable formal theorems from claims about mind-independent computational reality.
      ?

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    • 3.If P vs NP remains open, the semantic content of 'proper subset' in complexity theory may be underdetermined in ways that weaken extensional confidence in related hierarchy claims.
      ?

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    Reason for 2 of 2
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    • 1.The Time Hierarchy Theorem establishes separation only up to a constant factor overhead, and Blum's speedup theorem shows some functions resist any fixed complexity classification.
      ?

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    • 2.If speedup phenomena apply broadly, the inference from formal hierarchy theorems to stable containment relations between classes like P and TIME(f(n)) is not straightforwardly valid.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The Time Hierarchy Theorem part i) establishes proper containment between complexity classes under qualifying time bounds
      ?

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    • 2.Super-polynomial functions such as 2^(n^0.0001) or 2^(log(n)^2) satisfy the hypotheses of part i)
      ?

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