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    Parallel algorithms that achieve speedup only by employin... — Carmelics
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    Home/Skepticism
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    Parallel algorithms that achieve speedup only by employing exponentially many processors relative to input size are of little practical significance

    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.If parallel speedup requires exponentially many processors relative to input size, building a concrete computing device to implement such algorithms would be infeasible
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    • 2.Algorithms that cannot be concretely implemented have little practical significance
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.The threshold between 'practical' and 'impractical' is historically contingent: transistor counts once deemed impossible are now routine.
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    • 2.Exponential processor growth via quantum entanglement or biological substrates may render current feasibility intuitions obsolete.
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    • 3.Dismissing algorithms based on current hardware constraints conflates empirical engineering limits with principled computational significance.
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    Reason against 2 of 2
    ?
    • 1.Turing and Gandy's analyses show that abstract computational significance is logically independent of physical implementability constraints.
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    • 2.An algorithm's theoretical role in complexity class separations and reductions retains practical significance even without physical instantiation, as it bounds what efficient solutions must look like.
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    Related

    Algorithms that cannot be concretely implemented have little practical significa...An algorithm's theoretical role in complexity class separations and reductions r...Dismissing algorithms based on current hardware constraints conflates empirical ...Exponential processor growth via quantum entanglement or biological substrates m...
    +3 moreShow less
    If parallel speedup requires exponentially many processors relative to input siz...The threshold between 'practical' and 'impractical' is historically contingent: ...Turing and Gandy's analyses show that abstract computational significance is log...

    Similar

    Parallel algorithms that require exponentially many processors relativ...94%If a parallel algorithm achieves speedup only by employing exponential...89%If parallel algorithms achieve speedup only at the cost of exponential...89%Parallel computation using exponentially many processors relative to i...86%

    Source

    AI-extracted1/3 agreementValid
    SEP: computational-complexity
    View source passageHide passage
    \(\sc{TWO}\ \sc{PLAYER}\ \sc{SAT}_n\) may be shown to be complete for the class \(\Sigma^P_n\) in the Polynomial Hierarchy. Note, however, as the value of \(n\) increases, we expect that it should become more difficult to decide membership in \(\sc{TWO}\ \sc{PLAYER}\ \sc{SAT}_n\) in much the same way that it appears to become more difficult to determine whether a given player has a winning strategy for increasingly long games of Go or chess. This observation provides part of the reason why it is
    Extraction notes

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

    Details

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