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    Exponential time complexity is a sufficient condition for... — Carmelics
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    Home/Truth & Knowledge
    HistoryEditSee Inverse

    Exponential time complexity is a sufficient condition for classifying a decidable problem as intractable.

    Truth & Knowledge
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 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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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 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 against 2 of 2
    ?
    • 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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    Related

    A condition tied to a specific computational model cannot be a sufficient condit...Computational complexity classes are defined relative to deterministic Turing ma...Conflating worst-case asymptotic complexity with practical intractability commit...Exponential time on small inputs can be faster in practice than polynomial time ...
    +5 moreShow less
    It gradually came to be accepted within theoretical computer science that a prob...Many problems including SAT and TSP can easily be seen to admit exponential time...No polynomial time algorithm has been found for these problems despite sustained...Quantum algorithms (e.g., Shor's algorithm) solve problems in polynomial time th...Tractability is an empirical, context-sensitive notion concerning feasible solva...

    Similar

    Polynomial time decidability should be regarded as a positive criterio...86%It gradually came to be accepted within theoretical computer science t...84%To apply the Cobham-Edmonds Thesis and judge whether a problem X is fe...82%Possession of a polynomial time algorithm is sufficient grounds for re...81%

    Source

    AI-extracted1/3 agreementValid
    SEP: computational-complexity
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    The 1960s also saw a number of advances in algorithmic methods applicable to problems in fields like graph theory and linear algebra. One example was a technique known as dynamic programming. This method can sometimes be used to find efficient solutions to optimization problems which ask us to find an object which minimizes or maximizes a certain quantity from a range of possible solutions. An algorithm based on dynamic programming solves an instance of such a problem by recursively breaking it
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    Details

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    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit