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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that Members of the second machine class do not provide realistic representations of the complexity costs involved in concretely embodied computation

    ?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.Idealized machine models serve as mathematical abstractions that reveal structural complexity relationships independent of physical implementation details.
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      Think about whether this reason is strong or weak

    • 2.Turing's original formalization and subsequent Church-Turing thesis demonstrate that abstraction from physical substrate is methodologically legitimate and theoretically productive.
      ?

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    • 3.The P vs NP problem retains genuine mathematical significance regardless of whether RAM or pointer machines mirror concrete hardware constraints.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Hartmanis and Stearns established that complexity classes defined across different machine models are robustly equivalent up to polynomial factors, preserving the tractability/intractability distinction.
      ?

      Think about whether this reason is strong or weak

    • 2.If the relevant theoretical boundary is polynomial versus superpolynomial growth, then cross-model invariance under polynomial simulation is sufficient realism for complexity-theoretic purposes.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.It is widely believed that second machine class models can efficiently simulate non-deterministic computation in ways that conflate polynomial time, non-deterministic polynomial time, and polynomial space
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    • 2.Researchers including Chazelle, Monier, Schorr, and Vitányi have argued against the realism of second machine class models
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