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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that Whether a problem admits a polynomial time algorithm is independent of which model of computation is used to measure time complexity, across a broad class of reasonable models.

    ?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 Invariance Thesis presupposes a prior, non-formal notion of 'reasonable model' that smuggles in the conclusion it purports to establish.
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    • 2.Probabilistic, quantum, and analog models challenge the boundary of 'reasonable' in ways that make polynomial-time equivalence an open empirical question, not a logical truth.
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    • 3.Wilfried Sieg and others have shown that Church-Turing style invariance arguments require substantive physical assumptions that cannot be derived from mathematics alone.
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    Reason for 2 of 2
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    • 1.Hypercomputation theorists like Copeland and Shagrir argue that physically realizable systems may exist that transcend polynomial-time simulation by Turing machines.
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    • 2.If any physically instantiable model escapes polynomial-time mutual simulation, the class P is model-relative rather than model-invariant, undermining the claim's universality.
      ?

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    Reasons Against

    1 perspective
    Reason against
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    • 1.The Invariance Thesis holds that reasonable models can simulate each other within polynomial time overhead.
      ?

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    • 2.If one reasonable model solves a problem in polynomial time, the simulating model also solves it in polynomial time (since a polynomial composed with a polynomial is still a polynomial).
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