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    If intermediate values grow polynomially or worse, the to... — Carmelics
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    Challenges→Feasibility of computation is preserved when a function is defined by limited recursion on notation

    If intermediate values grow polynomially or worse, the total bit-complexity of the computation may escape feasibility even with few recursive steps.

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    Reasons For

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    Reason for
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    • 1.Bit-complexity compounds multiplicatively: polynomial growth in intermediate values directly increases digit counts across subsequent operations.
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    • 2.Even few recursions amplify complexity exponentially when bases are >1, making theoretical feasibility diverge sharply from practical computation.
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    • 3.Real hardware has fixed memory and time budgets; asymptotic analysis alone ignores constants that determine actual breakpoints in feasibility.
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    Reasons Against

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    • 1.Polynomial growth rates often remain manageable for realistic problem sizes; O(n³) doesn't become infeasible until n is quite large.
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    • 2.Modern arbitrary-precision arithmetic and specialized algorithms (FFT multiplication) reduce effective bit-complexity below naive worst-case bounds.
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    • 3.The claim conflates worst-case asymptotic behavior with typical performance; many recursive algorithms achieve feasibility despite intermediate growth.
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    Related

    Bit-complexity compounds multiplicatively: polynomial growth in intermediate val...Even few recursions amplify complexity exponentially when bases are >1, making t...Feasibility of computation is preserved when a function is defined by limited re...Modern arbitrary-precision arithmetic and specialized algorithms (FFT multiplica...
    +3 moreShow less
    Polynomial growth rates often remain manageable for realistic problem sizes; O(n...Real hardware has fixed memory and time budgets; asymptotic analysis alone ignor...The claim conflates worst-case asymptotic behavior with typical performance; man...

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