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It is not the case that Computational complexity theory requires complexity classes that are robust across different models of computation, whereas algorithmic analysis does not.
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Reasons For
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Reason for 1 of 2
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1.
The Church-Turing thesis establishes model-invariance for computability, but no analogous thesis has been proven for computational complexity.
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2.
Without a proven complexity-theoretic Church-Turing thesis, robustness across models remains an empirical regularity, not a principled requirement.
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3.
An empirical regularity cannot ground a categorical distinction between complexity theory and algorithmic analysis as a matter of conceptual necessity.
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Reason for 2 of 2
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1.
Knuth and the algorithmics tradition treats model-relative analysis as a virtue, not a defect, since real machines are not abstract models.
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2.
If robustness is achieved by abstracting away machine-specific constants, as in Cook-Karp reductions, then algorithmic analysis achieves analogous robustness via asymptotic notation.
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3.
The distinction between 'robust' complexity classes and asymptotic algorithmic analysis collapses into a difference of degree, not of kind.
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Reasons Against
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Reason against
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1.
Algorithmic analysis places primary emphasis on gauging the efficiency of specific algorithms for a given problem.
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2.
Complexity theory must consider the efficiency of all algorithms for solving a problem in order to classify problems by intrinsic difficulty.
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3.
Intrinsic difficulty classifications must not depend on an arbitrary choice of reference model.
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