The class F provides a machine-independent characterizati... — Carmelics

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The class F provides a machine-independent characterization of the complexity class FP

Proof of definition segments 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 class F is defined purely via a functional algebra without reference to Turing machines or any specific computational model
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2.The class F is extensionally equivalent to FP by Cobham's theorem
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Reasons Against

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Reason against 1 of 2

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1.Cobham's theorem establishes extensional equivalence, but extensional equivalence between classes does not entail that one characterization is machine-independent while the other is not.
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2.The functional algebra defining F implicitly encodes computational assumptions (e.g., bounded recursion on notation) that presuppose a binary representation tied to machine-level notions of input length.
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3.Putnam and Benacerraf's arguments about mathematical reduction show that multiple incompatible formalisms can be co-extensional, meaning equivalence underdetermines which characterization is the 'intrinsic' one.
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Reason against 2 of 2

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