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05:50:47 <esolangs> [[PL2 vCPU]] M https://esolangs.org/w/index.php?diff=87172&oldid=87104 * TeamLightning * (+22) /* Implementations */ changed GitHub link to point to main branch specifically
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07:46:52 <river> https://www.scottaaronson.com/blog/?p=5661
07:48:09 <river> > I noted that the BBB function grows uncomputably even given an oracle for the ordinary BB function. In fact, computing anything that grows as quickly as BBB is equivalent to solving any problem in the second level of the arithmetical hierarchy (where the computable functions are in the zeroth level, and the halting problem is in the first level)
07:48:10 <lambdabot> <hint>:1:108: error: parse error on input ‘,’
07:53:05 <river> the beeping busy beaver is very interesting
07:53:23 <river> how could 2nd level of the arithmetic hierarchy have influence on a function that gives finite numbers...
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09:36:08 <int-e> first level: phi(n) = exists k. psi(n, k), where psi is a sigma-0 sentence. second level: phi(n) = forall k. exists l. psi(n, k, l), again with a sigma-0 formula for psi... the latter is strictly more expressive...
09:37:29 <int-e> (The former is \Sigma_0^1; k can be viewed as a number of steps; the latter is \Pi_0^2, k can be viewed as the number of beeps, and l as the number of steps needed to reach the next beep.)
09:38:52 <int-e> (This is simplified though; in reality the variables need to encode whole TM runs with intermediate states.)
09:41:14 <int-e> that's just the corresponding halting problem
09:48:38 <int-e> The function version of these are phi(n,v) = exists k. psi(n, v, k) encoding f(n) = v; k is the encoding of a run of the TM (so potentially much larger than v) that produces v as an output, and phi(n, v) = forall k. exists l. psi(n, v, k, l), where for example, k is a partial run of the TM, and l extends it to the point where the TM beeps again.
09:49:46 <int-e> s/, and/. For the second level,/
10:06:37 <river> so it's kinda like halting but you count how many times it halts?
10:06:50 <river> but generalized so its not 'halting' but some arbitrary state
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13:34:01 <esolangs> [[User talk:A]] https://esolangs.org/w/index.php?diff=87173&oldid=70359 * Lyxal * (+64) /* A Question */ new section
13:34:30 <esolangs> [[User talk:A]] M https://esolangs.org/w/index.php?diff=87174&oldid=87173 * Lyxal * (+108)
13:35:30 <esolangs> [[User talk:A]] M https://esolangs.org/w/index.php?diff=87175&oldid=87174 * Lyxal * (+8)
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18:07:15 <esolangs> [[Special:Log/newusers]] create * Corbin * New user account
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18:16:18 <esolangs> [[Esolang:Introduce yourself]] M https://esolangs.org/w/index.php?diff=87176&oldid=87088 * Corbin * (+171) Introduce myself. It took a lot of effort to not use some variation of the Yoshikage Kira copypasta.
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19:40:57 <esolangs> [[NoCode]] N https://esolangs.org/w/index.php?oldid=87177 * Dominicentek * (+2149) Created page with "NoCode is an esoteric programming language written by [[User:Dominicentek]]. It doesn't have any source code. == How it works == This programming language has no syntax. It de..."
19:41:45 <esolangs> [[User:Dominicentek]] https://esolangs.org/w/index.php?diff=87178&oldid=87080 * Dominicentek * (+24)
19:50:30 <esolangs> [[User:Dominicentek]] https://esolangs.org/w/index.php?diff=87179&oldid=87178 * Dominicentek * (+4)
19:51:36 <esolangs> [[Language list]] https://esolangs.org/w/index.php?diff=87180&oldid=87157 * Dominicentek * (+12) /* N */
19:52:09 <esolangs> [[Language list]] https://esolangs.org/w/index.php?diff=87181&oldid=87180 * Dominicentek * (+0) /* N */
19:53:04 <esolangs> [[NoCode]] M https://esolangs.org/w/index.php?diff=87182&oldid=87177 * Dominicentek * (-13)
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23:47:39 <esolangs> [[NoCode]] M https://esolangs.org/w/index.php?diff=87183&oldid=87182 * PythonshellDebugwindow * (+117) /* Interpreter */ sum(map(lambda x: Cat, "Cats"))
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