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    Home/Original/inverse
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    Inverse View

    It is not the case that The class F provides a machine-independent characterization of the complexity class FP

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 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 for 2 of 2
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    • 1.Kreisel's squeezing argument requires that the informal concept being captured is already sufficiently determinate, but 'feasible computation' lacks the pre-theoretic determinacy needed to ground a machine-independence claim.
      ?

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    • 2.Without an independent grip on what feasible computation means apart from any formal model, the claim that F characterizes FP in a machine-independent way is circular rather than substantive.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 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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