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

    It is not the case that NP is a proper subset of NEXP

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.The Nondeterministic Time Hierarchy Theorem presupposes that nondeterministic computation is a coherent, well-defined model of physical possibility.
      ?

      Think about whether this reason is strong or weak

    • 2.The Church-Turing thesis underdetermines whether nondeterministic Turing machines correspond to any realizable computational process.
      ?

      Think about whether this reason is strong or weak

    • 3.A theorem whose premises invoke physically unrealizable models yields conclusions whose modal force is limited to mathematical, not computational, necessity.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.The inference from NTIME(t1) ⊊ NTIME(t2) to NP ⊊ NEXP conflates complexity classes defined by worst-case bounds with classes defined by problem families.
      ?

      Think about whether this reason is strong or weak

    • 2.Hartmanis and Stearns's original hierarchy theorems apply to specific machines, not to the robust, machine-independent classes NP and NEXP as standardly defined.
      ?

      Think about whether this reason is strong or weak

    • 3.Without a proof that the hierarchy theorem's machine-specific separations lift uniformly to relativization-resistant class separations, the proper subset claim outruns its formal justification.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    3 perspectives
    Reason against 1 of 3
    ?
    • 1.The Nondeterministic Time Hierarchy Theorem holds
      ?

      Think about whether this reason is strong or weak

    • 2.The functions n^k and 2^(n^k) satisfy the conditions of the Nondeterministic Time Hierarchy Theorem
      ?

      Think about whether this reason is strong or weak

    Reason against 2 of 3
    ?
    • 1.By the Non-deterministic Time Hierarchy Theorem, if t1(n+1)/t2(n) → 0 then NTIME(t1(n)) is a proper subset of NTIME(t2(n))
      ?

      Think about whether this reason is strong or weak

    • 2.The relevant polynomial and exponential functions satisfy this hypothesis
      ?

      Think about whether this reason is strong or weak

    Reason against 3 of 3
    ?
    • The Time Hierarchy Theorem part ii) implies proper containment between NP and NEXP
      ?

      Think about whether this reason is strong or weak

    Next step

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