See Jessica’s comment. Yeah it’s primitive recursive assuming that your deductive process is primitive recursive. (Also assuming that your traders are primitive recursive; e.g. if they are polytime as in the paper.) There’s probably some other parameters not necessarily set in the implementation described in the paper, e.g. the enumerator of trader-machines, but you can make those primrec.
If some function g is computable in O(f(n)) time for primitive recursive f then g is primitive recursive, by simulating a Turing machine. I am pretty sure a logical inductor would satisfy; while it’s super exponential time, it’s not so fast-growing it’s not primitive recursive (like with the Ackerman function).
Question for @Scott Garrabrant, @TsviBT, @Andrew_Critch, @So8res, @jessicata, and anyone else who knows the answer: the logical inductor constructed in the paper is not merely computable but also primitive recursive, right?
Seems obvious to me (because the fixed price point is approximated, etc), but I want to be sure I’m not missing something.
See Jessica’s comment. Yeah it’s primitive recursive assuming that your deductive process is primitive recursive. (Also assuming that your traders are primitive recursive; e.g. if they are polytime as in the paper.) There’s probably some other parameters not necessarily set in the implementation described in the paper, e.g. the enumerator of trader-machines, but you can make those primrec.
If some function g is computable in O(f(n)) time for primitive recursive f then g is primitive recursive, by simulating a Turing machine. I am pretty sure a logical inductor would satisfy; while it’s super exponential time, it’s not so fast-growing it’s not primitive recursive (like with the Ackerman function).