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    Parallel computation using exponentially many processors ... — Carmelics
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    Home/Skepticism
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    Parallel computation using exponentially many processors relative to input size would be of little practical significance

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    2 reasons against

    Reasons For

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    • If a parallel algorithm requires exponentially many processors relative to input size, there is little hope of building a computing device on which it could be concretely implemented
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    Reasons Against

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    Reason against 1 of 2
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    • 1.Physical realizability is not the sole criterion of theoretical significance; complexity classes defined by exponential parallelism illuminate fundamental structural boundaries in computation.
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    • 2.Valiant's work on NC and P-completeness demonstrates that the polynomial/exponential processor boundary has deep consequences for understanding which problems are inherently sequential, regardless of hardware constraints.
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    Reason against 2 of 2
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    • 1.The history of computing shows that resource bounds once deemed physically unrealizable have repeatedly become tractable as technology advances, as with quantum superposition exploiting exponential state spaces.
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    • 2.A claim of 'little practical significance' conflates present engineering limitations with permanent physical impossibility, a modal error that philosophers of science from Peirce onward have warned against in assessments of scientific possibility.
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    Related

    A claim of 'little practical significance' conflates present engineering limitat...If a parallel algorithm requires exponentially many processors relative to input...Physical realizability is not the sole criterion of theoretical significance; co...The history of computing shows that resource bounds once deemed physically unrea...
    +1 moreShow less
    Valiant's work on NC and P-completeness demonstrates that the polynomial/exponen...

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    Parallel algorithms that require exponentially many processors relativ...93%Parallel algorithms that achieve speedup only by employing exponential...86%If a parallel algorithm requires exponentially many processors relativ...82%If a parallel algorithm achieves speedup only by employing exponential...79%

    Source

    AI-extracted1/3 agreementValid
    SEP: computational-complexity
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    Nonetheless, \(\mathfrak{P}\) is a useful theoretical model in that it provides a formal medium for implementing procedures which call for certain operations to be carried out simultaneously in parallel. g. , Papadimitriou 1994). But this observation would still be of little practical significance if the algorithms in question achieved such speed up only at the cost of having to employ exponentially many processors relative to the size of their inputs. For in this case it seems that we would hav
    Extraction notes

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

    Details

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