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    Whether a problem admits a polynomial time algorithm is i... — Carmelics
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    Home/Modality & Possibility
    HistoryEditSee Inverse

    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.

    Modality & PossibilityTruth & 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.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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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 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 against 2 of 2
    ?
    • 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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    Topics

    Modality & PossibilityTruth & Knowledge

    Connections

    2 linked claims · 1 topic

    Causation1 linked
    The Invariance Thesis implies that whether a problem admits a polynomial time al...The Invariance Thesis shows that whether a problem admits a polynomial time algo...

    Related

    Hypercomputation theorists like Copeland and Shagrir argue that physically reali...If any physically instantiable model escapes polynomial-time mutual simulation, ...If one reasonable model solves a problem in polynomial time, the simulating mode...Probabilistic, quantum, and analog models challenge the boundary of 'reasonable'...
    +5 moreShow less
    The Invariance Thesis holds that reasonable models can simulate each other withi...The Invariance Thesis implies that whether a problem admits a polynomial time al...

    Similar

    The Invariance Thesis shows that whether a problem admits a polynomial...96%The Invariance Thesis implies that whether a problem admits a polynomi...96%If one reasonable model solves a problem in polynomial time, the simul...84%In many cases where no polynomial time algorithm is known, there is al...84%

    Source

    AI-extracted1/3 agreementValid
    SEP: computational-complexity
    View source passageHide passage
    In particular, a RAM machine \(A\) consists of a finite sequence of instructions (or program) \(\langle \pi_1,\ldots,\pi_n \rangle\) expressing how numerical operations (typically addition and subtraction) are to be applied to a sequence of registers \(r_1,r_2, \dots\) in which values may be stored and retrieved directly by their index. Showing that one of these models \(\mathfrak{M}_1\) determines the same class of functions as some reference model \(\mathfrak{M}_2\) (such as \(\mathfrak{T}\))
    Extraction notes

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

    Details

    The Invariance Thesis presupposes a prior, non-formal notion of 'reasonable mode...
    The Invariance Thesis shows that whether a problem admits a polynomial time algo...
    Wilfried Sieg and others have shown that Church-Turing style invariance argument...
    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit