Le jeu. 3 déc. 2020 à 01:37, Mike Stay <metaweta@gmail.com> a écrit :
In the end, this all boils down to Kolmogorov complexity, which depends on the choice of language.
Yes and no, Kolmogorov complexity is universal in the sense that it depends on the language or machine only up to a constant. But I feel you didn't reply to what I wrote, specifically what I think is the the core idea: the function f : R -> R which yields a map A(f) from reals to integer sequences, A(f) : R -> Z^N ; c -> a = (floor(f^n(c))) = (floor(c), floor(f(c)), floor(f(f(c))), ...) which should be continuous (i.e., constants c, c' which are sufficiently close should produce integer sequences with as many common terms as possible) but still "efficiently" code these sequences, which might translate to a differential function with a large derivative. But yes, thinking about it in these clarified mathematical terms shows that we have a kind of dilemma, if we get many primes with not so many decimals of c = c(primes), then probably it will / must(?) do less well for a different sequence.... So IMHO, rather than a sequence, we must fix the test cases on which the function is to be evaluated. Where "evaluation" is as specified in my earlier mail, the (asymptotic?) ratio of number of correct terms of the sequence, per number of correct digits in c. Maybe you can "reverse engineer" that scoring system by knowing the test suite if it is finite, (i.e., your function f would guess which sequence is "wanted" for a given constant c and artificially produce the required terms) but for a sufficiently well conceived infinite test suite, I doubt that would be possible. - Maximilian