NP-complete problems are widely believed to lack polynomi... — Carmelics

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NP-complete problems are widely believed to lack polynomial time algorithms

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Reasons For

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Reason for

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1.Extensive effort has been devoted to finding efficient solutions for NP-complete problems such as INTEGER PROGRAMMING and TSP without success
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2.The existence of a polynomial time algorithm for any NP-complete problem would imply P = NP, which runs strongly counter to expectation
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Reasons Against

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Reason against 1 of 2

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1.Absence of discovered polynomial algorithms after finite search constitutes inductive, not deductive, evidence against their existence.
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2.Hume's problem of induction entails that no finite record of failures licenses a nomological conclusion about algorithmic impossibility.
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3.The supporting argument thus conflates pragmatic expectation with ontological fact, a distinction central to Peirce's fallibilism.
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Reason against 2 of 2

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