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    If P ⊊ NP, then NP-complete problems are not in P. — Carmelics
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    Supports→Showing that a problem X is NP-complete establishes that no feasible algorithm for X can exist (assuming P ≠ NP).

    If P ⊊ NP, then NP-complete problems are not in P.

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    Problems not in P are not feasibly solvable under the Cobham-Edmonds thesis.Showing that a problem X is NP-complete establishes that no feasible algorithm f...The Cobham-Edmonds thesis identifies feasibility with polynomial-time computabil...

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    [21] It also follows from the transitivity of \(\leq_P\) that the existence of a polynomial time algorithm for even one \(\textbf{NP}\)-complete problem would entail the existence of polynomial time algorithms for all problems in \(\textbf{NP}\). The existence of such an algorithm would thus run strongly counter to expectation in virtue of the extensive effort which has been devoted to finding efficient solutions for particular \(\textbf{NP}\)-complete problems such as \(\sc{INTEGER}\ \sc{PROGRA

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