Now I'm wondering: could a monkey hitting random keys on a keyboard for an infinite amount of time eventually come up with the right prompts to get GPT-4 to produce code that compiles to a faithful reproduction of Doom?
If the random number generator is pseudo-random, this makes GPT-4 a deterministic finite-state machine, and the output sequence does not necessarily contain all possible subsequences no matter how many times the monkey types a new random key. Put differently, some output subsequences may be inaccessible no matter which keys are input. Same if the random number generator is truly random but its value cannot select among all possible output tokens, only a subset provided by the GPT at each step.