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    Hartmanis and Stearns's foundational work shows complexit... — Carmelics
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    Challenges→The existence of a polynomial time algorithm for any single NP-complete problem would entail the existence of polynomial time algorithms for all problems in NP.

    Hartmanis and Stearns's foundational work shows complexity classes are defined relative to machine models, so 'polynomial time' is not a robust absolute property immune to variation in computational substrate.

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    Key Terms

    Complexity classes(as used in computer science and philosophy of computation)
    In computer science, groups of problems sorted by how hard they are to solve—roughly, how much computing power and time they require.
    Computational substrate(in discussions of how computing systems are built)
    The physical or technological foundation that actually does the computing—like whether you're using a traditional computer, a quantum computer, or some other device.
    Hartmanis and Stearns(as founders of computational complexity theory)
    Two computer scientists who developed an important framework for understanding how much computational effort (time or memory) different types of problems require to solve.
    Machine models(as used in theoretical computer science)
    Different theoretical designs or frameworks for how computers process information, like imagining a computer that works in one way versus another way.

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    Robust(in the discussion of mathematical properties)
    Strong, reliable, and stable—something that doesn't break or change significantly when conditions vary slightly.
    polynomial time(Used to characterize feasible computation)
    Computational time complexity expressed as t(x)=x^c, where c is a constant and x is the length of the input

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    The existence of a polynomial time algorithm for any single NP-complete problem ...

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