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    Razborov and Rudich's natural proofs barrier presupposes ... — Carmelics
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    Challenges→A proof of P ≠ NP is beyond the reach of currently known proof techniques.

    Razborov and Rudich's natural proofs barrier presupposes strong pseudorandom function assumptions; if one-way functions do not exist, the barrier dissolves.

    ?Rate how convincing each reason is below to see the overall strength.
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    1 reason against

    Reasons For

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    Reason for
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    • 1.Natural proofs rely on constructivity: they need efficient algorithms to recognize hard functions, which PRFs provide by definition.
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    • 2.If one-way functions don't exist, P=NP becomes plausible, making all functions efficiently computable and barriers to lower bounds moot.
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    • 3.The barrier's core mechanism—avoiding help from non-constructive properties—presupposes cryptographic hardness assumptions.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Natural proofs restrictions apply structurally regardless of PRF existence; they constrain proof techniques, not only cryptographic assumptions.
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    • 2.Even without one-way functions, combinatorial barriers from natural proofs remain because they follow from relativization and algebrization principles.
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    • 3.The barrier's hardness derives partly from definitional obstacles to analyzing circuits, independent of whether PRFs or OWFs exist.
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    Related

    A proof of P ≠ NP is beyond the reach of currently known proof techniques.Even without one-way functions, combinatorial barriers from natural proofs remai...If one-way functions don't exist, P=NP becomes plausible, making all functions e...Natural proofs rely on constructivity: they need efficient algorithms to recogni...
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    Natural proofs restrictions apply structurally regardless of PRF existence; they...The barrier's core mechanism—avoiding help from non-constructive properties—pres...The barrier's hardness derives partly from definitional obstacles to analyzing c...

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