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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 Reasonable models of computation can simulate each other within a polynomially bounded overhead in time and a constant-factor overhead in space (Invariance Thesis).

    ?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 Invariance Thesis is a stipulative definition of 'reasonable model,' not an empirically discovered invariant, making it circular.
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      Think about whether this reason is strong or weak

    • 2.Models like quantum computers or analog machines with real-valued states are excluded by fiat, not by principled argument.
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    • 3.Bernstein and Vazirani (1997) showed quantum computers solve certain problems with exponential speedup, violating polynomial simulation bounds.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.The O(t(n)^3) simulation overhead between RAM machines and Turing machines conflates physical resource costs with abstract step counts.
      ?

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    • 2.Slot and van Emde Boas (1988) themselves noted that space measures are not robustly invariant across models, undermining the thesis's universality.
      ?

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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.A RAM machine can simulate a Turing machine with time overhead O(t(n)^3) and space overhead O(s(n)).
      ?

      Think about whether this reason is strong or weak

    • 2.Efficient simulations between a wide class of computation models—including Turing machine variants with multiple heads, tapes, and auxiliary storage—have been found.
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    • 3.Showing that model M1 simulates model M2 yields explicit time and space overhead functions extractable from the simulation construction.
      ?

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    Reason against 2 of 2
    ?
    • 1.Demonstrating that two computational models compute the same class of functions requires constructing a simulation where each basic step of one model is simulated by one or more steps of the other.
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      Think about whether this reason is strong or weak

    • 2.From the definition of a simulation between models, time and space overhead functions can be extracted such that computations in one model can be reproduced in another within those overhead bounds.
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    • 3.Efficient simulations between models such as RAM machines and Turing machines have been concretely found, with overhead bounds of O(t(n)^3) in time and O(s(n)) in space (Slot and Emde Boas 1988).
      ?

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