Unfortunately, you cannot prove whether or not an arbitrary program will terminate, meaning the best this scheme will do is provide an upper bound for KC.
Without waiting forever there’s no way of knowing if one of the programs smaller than that bound, which hasn’t terminated yet, isn’t going to eventually terminate and output the string.
Unfortunately, you cannot prove whether or not an arbitrary program will terminate, meaning the best this scheme will do is provide an upper bound for KC.
Without waiting forever there’s no way of knowing if one of the programs smaller than that bound, which hasn’t terminated yet, isn’t going to eventually terminate and output the string.
Yes, that’s the loophole for Manfred’s scheme (if I haven’t read into his comment something he didn’t intend).