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    Parallel algorithms that require exponentially many proce... — Carmelics
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    Parallel algorithms that require exponentially many processors relative to input size are of little practical significance

    SkepticismTruth & Knowledge
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
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    • If a parallel algorithm achieves speedup only by employing exponentially many processors relative to input size, there is little hope of building a concrete computing device to implement it
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.Practical significance is indexed to current technological constraints, which are historically contingent and subject to radical revision.
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    • 2.Quantum computing architectures can implement certain forms of massive parallelism without requiring exponentially many discrete physical processors.
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    • 3.A claim about practical limits grounded in present engineering bounds conflates empirical limitation with principled impossibility.
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    Reason against 2 of 2
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    • 1.Theoretical algorithms of 'little practical significance' have repeatedly driven foundational insights that later became practically indispensable, as Turing's halting problem work illustrates.
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    • 2.The criterion of practical significance cannot be the sole arbiter of theoretical value in complexity theory without collapsing the descriptive project into engineering.
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    Related

    A claim about practical limits grounded in present engineering bounds conflates ...If a parallel algorithm achieves speedup only by employing exponentially many pr...Practical significance is indexed to current technological constraints, which ar...Quantum computing architectures can implement certain forms of massive paralleli...
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    The criterion of practical significance cannot be the sole arbiter of theoretica...Theoretical algorithms of 'little practical significance' have repeatedly driven...

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    Parallel algorithms that achieve speedup only by employing exponential...94%Parallel computation using exponentially many processors relative to i...93%If a parallel algorithm requires exponentially many processors relativ...87%If a parallel algorithm achieves speedup only by employing exponential...84%

    Source

    AI-extracted1/3 agreementValid
    SEP: computational-complexity
    View source passageHide passage
    Consider, for instance the following variation on the standard rules of Go: (i) the game is played on an \(n \times n\) board; (ii) the winner of the game is the player with the most stones at the end of \(n^2\) rounds. e. the player who moves first)? [30] What these games have in common is that the definition of a winning strategy for the player who moves first involves the alternation of existential and universal quantifiers in a manner which mimics the definition of the classes \(\Sigma^P_n\)
    Extraction notes

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

    Details

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