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    Carmelics

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

    It is not the case that Adding non-determinism to the deterministic Turing machine model does not enlarge the class of decidable problems

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.The identification of 'decidability' with recursive enumerability presupposes Church-Turing Thesis, which remains a thesis, not a proven theorem.
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    • 2.If hypercomputation models (Malament-Hogarth spacetimes, accelerating Turing machines) are physically realizable, non-determinism may access super-recursive classes unavailable to standard DTMs.
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    • 3.Equating both models to 'recursive problems' inherits the thesis's assumption that no physically possible process exceeds Turing-computable functions.
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    Reason for 2 of 2
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    • 1.The proof of NTM-DTM decidability equivalence relies on simulation arguments that collapse non-deterministic branching into deterministic search, preserving halting but not computational meaning.
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      Think about whether this reason is strong or weak

    • 2.Philosophical accounts of non-determinism rooted in quantum indeterminacy or modal realism (Lewis) treat branching as ontologically irreducible, not merely epistemically unexplored.
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    • 3.If non-deterministic choice is genuinely ontological rather than epistemic, the simulation argument conflates decision-theoretic equivalence with metaphysical equivalence of computational process.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The class of problems decidable by non-deterministic Turing machines is exactly the recursive problems
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    • 2.The class of problems decidable by deterministic Turing machines is also exactly the recursive problems
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