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    Reduction-based arguments assume that computational probl... — Carmelics
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    Challenges→If any NP-complete problem has a polynomial time algorithm, then all problems in NP have polynomial time algorithms

    Reduction-based arguments assume that computational problems have determinate, mind-independent identity conditions across different encodings.

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    1 reason for
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    Reasons For

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    Reason for
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    • 1.Computational problems like 'sorting' have mathematical definitions independent of how we represent them in code or hardware.
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    • 2.If identity were encoding-dependent, the same algorithm couldn't be correctly implemented in different programming languages.
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    • 3.Problem reduction (e.g., SAT to 3-SAT) presupposes problems have stable identities across transformations, enabling valid comparison.
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    Reasons Against

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    Reason against
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    • 1.Computational complexity depends partly on encoding: binary vs. unary representation changes problem difficulty fundamentally.
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    • 2.What counts as 'the same problem' is partly determined by our practical interests and choice of representation scheme, not mind-independent facts.
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    • 3.Reduction arguments work pragmatically without requiring determinate, encoding-independent identity conditions for problems.
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    Truth & Knowledge1 linkedModality & Possibility1 linked

    Related

    Computational complexity depends partly on encoding: binary vs. unary representa...Computational problems like 'sorting' have mathematical definitions independent ...If any NP-complete problem has a polynomial time algorithm, then all problems in...If identity were encoding-dependent, the same algorithm couldn't be correctly im...
    +3 moreShow less
    Problem reduction (e.g., SAT to 3-SAT) presupposes problems have stable identiti...Reduction arguments work pragmatically without requiring determinate, encoding-i...What counts as 'the same problem' is partly determined by our practical interest...

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    Perspectives
    2 (1 for, 1 against)
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