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    Without specifying whether the reduction is many-one, Tur... — Carmelics
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    Challenges→If P = NP, then finding a satisfying valuation for a propositional formula would be no harder than constructing its truth table

    Without specifying whether the reduction is many-one, Turing, or Cook, the comparative difficulty relation invoked is semantically underdetermined and cannot bear the logical weight the argument assigns it.

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    Key Terms

    Comparative difficulty relation(in logic and problem-solving)
    A way of comparing how hard or complex different things are relative to each other.
    Cook(in computer science history)
    Stephen Cook is a computer scientist who developed 'Cook reduction' (also called polynomial-time reduction), another method for comparing how hard computational problems are to solve.
    Logical weight(in argumentation and logic)
    The importance or strength of an argument—how much evidence or reasoning it carries to support a conclusion.
    Reduction (many-one, Turing, Cook)(in logic and computer science)
    Different mathematical methods for showing that one problem can be transformed into another problem. They're named after logicians and computer scientists who developed them, and they help determine how difficult problems are to solve.

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    Semantically underdetermined(in philosophy of language)
    When something doesn't have a clear, definite meaning—there's not enough information to pin down exactly what it's supposed to mean.
    Turing
    # Turing Alan Turing was a British mathematician and scientist (1912-1954) who is considered the father of computer science and artificial intelligence. He invented the "Turing Machine," a theoretical device that helped define what computers could and couldn't do, and created the "Turing Test," a famous challenge to determine whether a machine can exhibit intelligent behavior indistinguishable from a human. His groundbreaking work during World War II on code-breaking, combined with his pioneering ideas about thinking machines, made him one of the most influential thinkers of the 20th century.

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    Proof of definition segments1 linkedTruth & Knowledge1 linked

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    If P = NP, then finding a satisfying valuation for a propositional formula would...

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