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
    Complexity classes like P are closed under complementation — Carmelics
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Truth & Knowledge
    HistoryEditSee Inverse

    Complexity classes like P are closed under complementation

    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.For a deterministic machine, acceptance and rejection conventions are symmetric
      ?

      Think about whether this reason is strong or weak

    • 2.For a deterministic machine T to accept or reject an input x, it is both necessary and sufficient that there exist a single halting computation
      ?

      Think about whether this reason is strong or weak

    • 3.The output is determined by whether the final configuration is accepting or rejecting
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.The symmetry between acceptance and rejection in P assumes a fixed encoding, but complementation requires that 'non-membership' is itself a decidable property.
      ?

      Think about whether this reason is strong or weak

    • 2.Complexity theorists like Ladner and Lynch distinguish between syntactic and semantic closure properties, and P's closure under complement is a syntactic artifact of determinism, not a universal logical truth about decidability.
      ?

      Think about whether this reason is strong or weak

    • 3.The claim conflates computational convention with logical necessity: flipping accept/reject states produces a correct complement machine only if the original machine halts on all inputs, which is a substantive assumption about total functions.
      ?

      Think about whether this reason is strong or weak

    Reason against 2 of 2
    ?
    • 1.Oracle-relative results (Baker, Gill, Solovay 1975) demonstrate that structural properties like closure under complement can fail or hold contingently depending on the computational environment.
      ?

      Think about whether this reason is strong or weak

    • 2.If closure under complementation were a deep logical truth grounded in determinism's symmetry, it would be invariant across all relativizations, but oracle constructions show this closure is not invariant in analogous nondeterministic settings precisely because symmetry breaks.
      ?

      Think about whether this reason is strong or weak

    Sign in or register to share your perspective on this statement.

    Next step

    Based on where you are in your exploration

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

    Topics

    Truth & Knowledge

    Connections

    2 topics

    Modality & Possibility2 linkedCausation1 linked

    Related

    Complexity theorists like Ladner and Lynch distinguish between syntactic and sem...For a deterministic machine T to accept or reject an input x, it is both necessa...For a deterministic machine, acceptance and rejection conventions are symmetricIf closure under complementation were a deep logical truth grounded in determini...
    +4 moreShow less
    Oracle-relative results (Baker, Gill, Solovay 1975) demonstrate that structural ...The claim conflates computational convention with logical necessity: flipping ac...The output is determined by whether the final configuration is accepting or reje...The symmetry between acceptance and rejection in P assumes a fixed encoding, but...

    Similar

    The class P is closed under complementation (P = coP)96%P is closed under complementation91%NP is not known to be closed under complementation88%There is no a priori guarantee that NP is closed under complementation...82%

    Source

    AI-extracted1/3 agreementValid
    SEP: computational-complexity
    View source passageHide passage
    In contrast to the non-deterministic Turing machine model \(\mathfrak{N}\), the acceptance and rejection conventions for deterministic models of computation such as \(\mathfrak{T}\) are symmetric. In other words, for a deterministic machine \(T\) to either accept or reject an input \(x\), it is both necessary and sufficient that there exist a single halting computation \(C_0(x),\ldots,C_n(x)\). The output of the machine is then determined by whether \(C_n(x)\) is an accepting or rejecting config
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

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