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    Inverse View

    It is not the case that Polynomial-time reducibility preserves decision-problem solvability in principle, but the reduction itself may introduce constant or hidden complexity factors that render the composed algorithm impractical even if formally polynomial.

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    Reasons For

    1 perspective
    Reason for
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    • 1.Polynomial-time reducibility is defined precisely to avoid hidden complexity: if A reduces to B in poly-time, solving B solves A without exponential blowup.
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    • 2.Impracticality due to large constants is a separate issue from solvability-in-principle; conflating them misuses the theoretical concept of polynomial reduction.
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    • 3.Most natural NP-complete reductions (e.g., Cook-Levin) do introduce overhead, but this reflects problem hardness, not a flaw in reducibility as a formal tool.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.A 3SAT instance reduced to clique via polynomial reduction may require checking exponentially many cliques despite polynomial-bounded reduction overhead.
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    • 2.Constants hidden in Big-O notation (e.g., O(n^100)) can make formally polynomial algorithms computationally infeasible for all practical input sizes.
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    • 3.Chained reductions compound overhead multiplicatively: if each of k reductions adds factor c, total complexity multiplies by c^k even in polynomial class.
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