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    Home/Original/inverse
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    Inverse View

    It is not the case that 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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    Reasons For

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    Reason for
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    • 1.NC/P distinction relies on worst-case analysis; many P-complete problems admit efficient average-case or approximation solutions that bypass sequentiality.
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    • 2.The claim conflates theoretical parallelism limits with practical hardware constraints—quantum computing or novel architectures might bypass these theoretical boundaries.
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    • 3.Defining 'inherently sequential' via polynomial-time formalism assumes classical computation models; it says nothing about what's fundamental to problem structure itself.
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    Reasons Against

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    Reason against
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    • 1.NC-completeness identifies problems requiring sequential dependencies that parallelization cannot overcome, revealing fundamental computational bottlenecks.
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    • 2.P-completeness theory distinguishes problems solvable efficiently from those with inherent sequential structure, independent of implementation technology.
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    • 3.Valiant's framework formalizes the intuition that some problems (like circuit evaluation) fundamentally require sequential steps no matter hardware parallelism.
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