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    Home/Original/inverse
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    Inverse View

    It is not the case that Parallel algorithms that achieve speedup only by employing exponentially many processors relative to input size are of little practical significance

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    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 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 for 2 of 2
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    • 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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    Reasons Against

    1 perspective
    Reason against
    ?
    • 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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