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    Made withinDC&Austin
    Statements
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    Perspectives
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    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that PSPACE equals NPSPACE

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Savitch's Theorem establishes an inclusion relation between complexity classes, not their equality, leaving open whether PSPACE is a proper subset of NPSPACE.
      ?

      Think about whether this reason is strong or weak

    • 2.The argument conflates 'NPSPACE ⊆ PSPACE' (derivable from Savitch) with 'PSPACE = NPSPACE', which requires the converse inclusion as a separate premise.
      ?

      Think about whether this reason is strong or weak

    • 3.The converse inclusion PSPACE ⊆ NPSPACE, while intuitive, is a definitional observation that must be stated explicitly to complete the biconditional equality claim.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Complexity-theoretic equalities derived from asymptotic containment results inherit the epistemic limitations of worst-case analysis, as Aaronson and others have noted.
      ?

      Think about whether this reason is strong or weak

    • 2.Savitch's quadratic blowup does not preclude the existence of problems in NPSPACE requiring strictly superpolynomial deterministic space on a measure-theoretic majority of inputs.
      ?

      Think about whether this reason is strong or weak

    • 3.An equality claim grounded solely in worst-case asymptotic bounds may be extensionally correct yet fail to capture the intensional computational distinction between nondeterministic and deterministic space.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.For any space constructible function s(n), NSPACE(s(n)) is a subset of SPACE((s(n))^2)
      ?

      Think about whether this reason is strong or weak

    • 2.Savitch's Theorem holds
      ?

      Think about whether this reason is strong or weak

    Reason against 2 of 2
    ?
    • 1.By Savitch's Theorem, NSPACE(s(n)) is a subset of SPACE((s(n))^2) for any space constructible s(n)
      ?

      Think about whether this reason is strong or weak

    • 2.Squaring a polynomial still yields a polynomial, so NPSPACE does not exceed PSPACE
      ?

      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.