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    Order-invariant definability in FO(LFP) diverges from ord... — Carmelics
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    Challenges→P ≠ NP if and only if there exists a class of ordered structures definable in existential second-order logic which is not definable by a formula of FO(LFP)

    Order-invariant definability in FO(LFP) diverges from ordered FO(LFP) definability, making the logical capture of P order-sensitive.

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    1 reason for
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    Reasons For

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    Reason for
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    • 1.Order-invariant definability requires properties invariant across all orderings, a strictly stronger constraint than ordered definability.
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    • 2.P-completeness results depend on specific orderings; absent order-invariance, FO(LFP) captures only order-dependent fragments of P.
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    • 3.This divergence reveals that canonical logical characterizations of P require order structure, supporting order-sensitivity of computational complexity.
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    Reasons Against

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    Reason against
    ?
    • 1.Order-invariant and ordered FO(LFP) may capture identical problems; divergence in definability doesn't entail divergence in expressive power.
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    • 2.The practical relevance of order-invariance is unclear—real computation doesn't privilege order-independent definitions over order-dependent ones.
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    Related

    Order-invariant and ordered FO(LFP) may capture identical problems; divergence i...Order-invariant definability requires properties invariant across all orderings,...P ≠ NP if and only if there exists a class of ordered structures definable in ex...P-completeness results depend on specific orderings; absent order-invariance, FO...
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    The practical relevance of order-invariance is unclear—real computation doesn't ...This divergence reveals that canonical logical characterizations of P require or...

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    2 (1 for, 1 against)
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