Feasibility is preserved under limited recursion on notation — Carmelics

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Feasibility is preserved under limited recursion on notation

Modality & Possibility Truth & Knowledge

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1 reason for

2 reasons against

Reasons For

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Reason for

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1.The basis functions F_0 are feasibly computable
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2.Feasibility is preserved under composition
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3.When f(x,y) is defined by limited recursion on notation, the number of recursive steps is proportional to the length of y's binary representation rather than to the value of y itself
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Reasons Against

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Reason against 1 of 2

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1.The polynomial bound on auxiliary functions presupposes a fixed machine model, but feasibility judgments are model-relative in ways that undermine universal closure claims.
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2.Cobham's original characterization of feasibility via limited recursion on notation tacitly assumes sequential computation, excluding parallel models where the bound fails to generalize.
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Reason against 2 of 2

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