Skip to content
Carmelics
TopicsThinkersChangesContributorsLoading account…

    Carmelics

    A reasoning platform. Break down any belief into clear reasons, explore both sides, and weigh the evidence honestly.

    Navigate

    • Topics
    • Search
    • Recent Changes
    • Contribute
    • How It Works
    • Glossary
    • Thinkers
    • Contributors
    • About
    • Statistics
    • Terms
    • Privacy

    Database

    Statements
    —
    Perspectives
    —
    Topics
    —

    Press ? for keyboard shortcuts

    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that Polynomial time computability captures the boundary of feasible computability (quasi-inductive argument for CET).

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Polynomial time includes algorithms with degree-1000 polynomials that are practically infeasible on any physical hardware within cosmological timescales.
      ?

      Think about whether this reason is strong or weak

    • 2.Sub-polynomial algorithms (e.g., quasi-polynomial) or fixed-parameter tractable algorithms solve many 'intractable' problems for real-world input distributions.
      ?

      Think about whether this reason is strong or weak

    • 3.The quasi-inductive argument conflates mathematical tractability classes with empirical feasibility, committing a category error Hartmanis and Stearns's original complexity theory never intended.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Average-case complexity, not worst-case polynomial time, determines practical feasibility, as Levin's average-case complexity theory and cryptographic practice demonstrate.
      ?

      Think about whether this reason is strong or weak

    • 2.Many NP-complete problems are routinely solved in practice via SAT solvers and heuristics, meaning worst-case intractability fails to track the actual boundary of feasible computation.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.In cases where a function can be uniformly computed for the class of instances of practical concern, this is typically because a polynomial time algorithm has been discovered that can be implemented on current hardware.
      ?

      Think about whether this reason is strong or weak

    • 2.In cases where a function cannot be uniformly computed for all arguments of practical interest, a polynomial time algorithm has typically not been discovered.
      ?

      Think about whether this reason is strong or weak

    • 3.In many practically intractable cases, there also exists circumstantial evidence that no polynomial time algorithm can exist.
      ?

      Think about whether this reason is strong or weak

    Next step

    Based on where you are in your exploration

    Strongest counterpoint
    Explore the most compelling reason on the other side.