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    Complexity-theoretic equalities derived from asymptotic c... — Carmelics
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    Challenges→PSPACE equals NPSPACE

    Complexity-theoretic equalities derived from asymptotic containment results inherit the epistemic limitations of worst-case analysis, as Aaronson and others have noted.

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    Reasons For

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    • 1.Worst-case complexity bounds often ignore typical instance structure, making asymptotic results poor predictors of practical algorithm behavior.
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    • 2.Aaronson's work on average-case and smoothed complexity demonstrates that worst-case analysis can be misleading for real computational phenomena.
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    • 3.P vs NP equalities derived solely from asymptotic containment inherit these limitations, lacking empirical grounding for finite instances.
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    Reasons Against

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    • 1.Worst-case analysis provides rigorous, model-independent guarantees that average-case metrics cannot match without additional distributional assumptions.
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    • 2.Asymptotic results establish necessary truths about algorithm classes regardless of epistemic limitations—they don't become false because analysis is incomplete.
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    • 3.Many practical algorithms have worst-case bounds matching average performance; the gap between theory and practice doesn't undermine theoretical equalities themselves.
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    Aaronson's work on average-case and smoothed complexity demonstrates that worst-...Asymptotic results establish necessary truths about algorithm classes regardless...Many practical algorithms have worst-case bounds matching average performance; t...P vs NP equalities derived solely from asymptotic containment inherit these limi...
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    PSPACE equals NPSPACEWorst-case analysis provides rigorous, model-independent guarantees that average...Worst-case complexity bounds often ignore typical instance structure, making asy...

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