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    Members of the second machine class do not provide realis... — Carmelics
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    Members of the second machine class do not provide realistic representations of the complexity costs involved in concretely embodied computation

    SkepticismTruth & Knowledge
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 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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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Idealized machine models serve as mathematical abstractions that reveal structural complexity relationships independent of physical implementation details.
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    • 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.
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    Reason against 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.
      ?

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    • 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.
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    Related

    Hartmanis and Stearns established that complexity classes defined across differe...Idealized machine models serve as mathematical abstractions that reveal structur...If the relevant theoretical boundary is polynomial versus superpolynomial growth...It is widely believed that second machine class models can efficiently simulate ...
    +3 moreShow less
    Researchers including Chazelle, Monier, Schorr, and Vitányi have argued against ...The P vs NP problem retains genuine mathematical significance regardless of whet...Turing's original formalization and subsequent Church-Turing thesis demonstrate ...

    Similar

    Members of the second machine class do not provide realistic represent...100%Experience has borne out that first machine class members accurately r...84%Formally demonstrating that the second machine class does not provide ...84%Formally demonstrating that second machine class models are unrealisti...82%

    Source

    AI-extracted1/3 agreementValid
    SEP: computational-complexity
    View source passageHide passage
    As \(\phi \in \sc{SAT}\) just in case a satisfying valuation exists, this is a correct method for deciding \(\sc{SAT}\) relative to conventions (i)–(iii) from above. This means that \(\sc{SAT}\) can be solved in polynomial time relative to \(\mathfrak{N}\). This example also illustrates why adding non-determinism to the original deterministic model \(\mathfrak{T}\) does not enlarge the class of decidable problems. [12] It is evident that if \(N\) has time complexity \(f(n)\), then \(T_N\) must
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit