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 Possession of a polynomial time decision algorithm is sufficient grounds for regarding a problem as feasibly decidable.

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.A polynomial algorithm with degree 100 or leading coefficient 10^50 is computationally infeasible on any physically realizable machine.
      ?

      Think about whether this reason is strong or weak

    • 2.Feasibility is an empirical and engineering concept tied to actual resource constraints, not an abstract worst-case asymptotic property.
      ?

      Think about whether this reason is strong or weak

    • 3.Cobham himself acknowledged that the identification of P with feasibility was a theoretical idealization, not a literal claim about practice.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.The Invariance Thesis establishes machine-independence of polynomial time only up to polynomial translation, which presupposes the very criterion it is meant to justify.
      ?

      Think about whether this reason is strong or weak

    • 2.Circular justification of a complexity class via a thesis that already encodes polynomial-time equivalence cannot ground the normative claim that P equals feasibility.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The Invariance Thesis implies that whether a problem admits a polynomial time algorithm is independent of which reasonable model of computation is used to measure time complexity.
      ?

      Think about whether this reason is strong or weak

    • 2.Polynomial time algorithms scale in a manner that remains tractable as input size grows, unlike exponential time algorithms.
      ?

      Think about whether this reason is strong or weak

    • 3.Cobham and Edmonds independently proposed this criterion as the positive counterpart to the intractability condition.
      ?

      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.