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ModelOfTheory's profile
Model Of Theory
Model Of Theory
Model Of Theory
@ModelOfTheory

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Model Of Theory

@ModelOfTheory

ZFC, THIS.

Joined July 2016

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    1. Shredder Rawflesh‏ @RadishHarmers 27 Jun 2017
      Replying to @RadishHarmers @ModelOfTheory

      The parenthetical should just say "or it is not provably surjective".

      1 reply 0 retweets 0 likes
    2. Model Of Theory‏ @ModelOfTheory 27 Jun 2017
      Replying to @RadishHarmers

      Polynomial time functions can be made provably total. But yes, 2nd condition says no provably surjective recursive function computes it.

      1 reply 0 retweets 0 likes
    3. Shredder Rawflesh‏ @RadishHarmers 27 Jun 2017
      Replying to @ModelOfTheory

      Right, I was just saying "computes its inverse" is needlessly wordy compared to "computes it".

      1 reply 0 retweets 0 likes
    4. Shredder Rawflesh‏ @RadishHarmers 27 Jun 2017
      Replying to @RadishHarmers @ModelOfTheory

      To code n which computes function f, we can easily associate code Inv(n) which computes f^{-1} (choosing, say, minimal preimages).

      1 reply 0 retweets 0 likes
    5. Shredder Rawflesh‏ @RadishHarmers 27 Jun 2017
      Replying to @RadishHarmers @ModelOfTheory

      Ah, but all these things you post are half the time impossibilities anyway, I forgot…

      1 reply 0 retweets 0 likes
    6. Model Of Theory‏ @ModelOfTheory 27 Jun 2017
      Replying to @RadishHarmers

      Inv(f) will compute a permutation, but might not be provably total. I think most of my math-related noun phrases are possible.

      1 reply 0 retweets 0 likes
    7. Shredder Rawflesh‏ @RadishHarmers 27 Jun 2017
      Replying to @ModelOfTheory

      In that case, I return to saying might as well just say "a permutation of N that is computable in polytime, but not provably (in ZFC) onto".

      1 reply 0 retweets 0 likes
    8. Shredder Rawflesh‏ @RadishHarmers 27 Jun 2017
      Replying to @RadishHarmers @ModelOfTheory

      I.e., a code for a polytime machine, which happens to be injective and surjective, but is not provably surjective.

      2 replies 0 retweets 0 likes
    9. Model Of Theory‏ @ModelOfTheory 27 Jun 2017
      Replying to @RadishHarmers

      I phrased it to mimic def of a 1-way function, without requirement of avg-case difficulty, but stronger requirement of worst-case difficulty

      1 reply 0 retweets 1 like
    10. Shredder Rawflesh‏ @RadishHarmers 27 Jun 2017
      Replying to @ModelOfTheory

      Ah, gotcha.

      1 reply 0 retweets 0 likes
      Model Of Theory‏ @ModelOfTheory 27 Jun 2017
      Replying to @RadishHarmers

      Actually, can prob make avg case hard too, in that no provably total recursive function agrees w/ f^-1 on non-negligible fraction of inputs.

      9:07 PM - 27 Jun 2017
      1 reply 0 retweets 0 likes
        1. Model Of Theory‏ @ModelOfTheory 27 Jun 2017
          Replying to @ModelOfTheory @RadishHarmers

          Important difference is that in definition of one-way function f, function to find x from f(x) also given length(x) in unary as parameter.

          0 replies 0 retweets 0 likes
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