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 If problem identity is encoding-relative, polynomial-time reducibility ≤_P does not transitively preserve the property of being 'the same computational task'.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Polynomial-time reductions are defined to work for any standard encoding; encoding choice doesn't affect computational class membership.
      ?

      Think about whether this reason is strong or weak

    • 2.If problem identity were truly encoding-relative, we couldn't meaningfully discuss NP-completeness, which assumes encoding-invariant identity.
      ?

      Think about whether this reason is strong or weak

    • 3.Transitivity failure would require A ≤_P B ≤_P C but A ≰_P C under same encoding—no standard example demonstrates this.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Problem identity depends on how we represent inputs/outputs; different encodings can obscure or reveal task structure differently.
      ?

      Think about whether this reason is strong or weak

    • 2.A ≤_P B and B ≤_P C doesn't guarantee A and C share the same computational essence if encoding choices differ at each reduction step.
      ?

      Think about whether this reason is strong or weak

    • 3.Transitivity assumes sameness is preserved, but encoding-relative identity means 'same task' is observer-dependent, not intrinsic.
      ?

      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.