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    PSPACE equals NPSPACE — Carmelics
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    Home/Truth & Knowledge
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    PSPACE equals NPSPACE

    Truth & Knowledge
    ?Rate how convincing each reason is below to see the overall strength.
    2 reasons for
    2 reasons against

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.For any space constructible function s(n), NSPACE(s(n)) is a subset of SPACE((s(n))^2)
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    • 2.Savitch's Theorem holds
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    Reason for 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)
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    • 2.Squaring a polynomial still yields a polynomial, so NPSPACE does not exceed PSPACE
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    Reasons Against

    2 perspectives
    Reason against 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.
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    • 2.The argument conflates 'NPSPACE ⊆ PSPACE' (derivable from Savitch) with 'PSPACE = NPSPACE', which requires the converse inclusion as a separate premise.
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    • 3.The converse inclusion PSPACE ⊆ NPSPACE, while intuitive, is a definitional observation that must be stated explicitly to complete the biconditional equality claim.
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    Reason against 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.
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    • 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.
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    • 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.
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    Related

    An equality claim grounded solely in worst-case asymptotic bounds may be extensi...By Savitch's Theorem, NSPACE(s(n)) is a subset of SPACE((s(n))^2) for any space ...Complexity-theoretic equalities derived from asymptotic containment results inhe...For any space constructible function s(n), NSPACE(s(n)) is a subset of SPACE((s(...
    +6 moreShow less
    Savitch's Theorem establishes an inclusion relation between complexity classes, ...Savitch's Theorem holdsSavitch's quadratic blowup does not preclude the existence of problems in NPSPAC...Squaring a polynomial still yields a polynomial, so NPSPACE does not exceed PSPA...The argument conflates 'NPSPACE ⊆ PSPACE' (derivable from Savitch) with 'PSPACE ...The converse inclusion PSPACE ⊆ NPSPACE, while intuitive, is a definitional obse...

    Similar

    P equals coP100%PSPACE equals NPSPACE (PSPACE = NPSPACE)95%If the F equals the G, and the F is H, then the G is H88%BHP is in P only if P equals NP84%

    Source

    AI-extracted1/3 agreementValid
    SEP: computational-complexity
    View source passageHide passage
    2 Complexity classes and the hierarchy theorems Recall that a complexity class is a set of languages all of which can be decided within a given time or space complexity bound \(t(n)\) or \(s(n)\) with respect to a fixed model of computation. g. non-recursive ones) it is standard to restrict attention to complexity classes defined when \(t(n)\) and \(s(n)\) are time or space constructible. e. a string of \(n\) 1s) halts after exactly \(t(n)\) steps. Similarly, \(s(n)\) is said to be space constru
    Extraction notes

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

    Details

    Type
    claim
    Perspectives
    4 (2 for, 2 against)
    Edits
    1 edit