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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that Exponential time complexity is a sufficient condition for classifying a decidable problem as intractable.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Computational complexity classes are defined relative to deterministic Turing machines, but physical computation need not be so constrained.
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    • 2.Quantum algorithms (e.g., Shor's algorithm) solve problems in polynomial time that classical models require exponential time for.
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    • 3.A condition tied to a specific computational model cannot be a sufficient condition for a model-independent property like 'intractability'.
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    Reason for 2 of 2
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    • 1.Exponential time on small inputs can be faster in practice than polynomial time on large inputs due to constant factors and problem structure.
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    • 2.Tractability is an empirical, context-sensitive notion concerning feasible solvability, not a purely formal property of worst-case asymptotic bounds.
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    • 3.Conflating worst-case asymptotic complexity with practical intractability commits the error Cobham and Edmonds warned against: mistaking mathematical elegance for physical reality.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Many problems including SAT and TSP can easily be seen to admit exponential time brute force algorithms.
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    • 2.No polynomial time algorithm has been found for these problems despite sustained effort in the 1960s and 1970s.
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    • 3.It gradually came to be accepted within theoretical computer science that a problem is intractable when the most efficient algorithm solving it has at best exponential time complexity.
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    Strongest counterpoint
    Explore the most compelling reason on the other side.