In a single run, obviously not any, because it's context window is very limited. With a loop and access to an "API" (or willing conversation partner agreeing to act as one) to operate a Turing tape mechanism? It becomes a question of ability to coax it into complying. It trivially has the ability to carry out every step, and your main challenge becomes to get it to stick to it over and over.
One step "up", you can trivially get GPT4 to symbolically solve fairly complex runs of instructions of languages it can never have seen before if you specify a grammar and then give it a program, with the only real limitation again being getting it to continue to adhere to the instructions for long enough before it starts wanting to take shortcuts.
In other words: It can compute any computable function about as well as a reasonably easily distractable/bored human.
In a single run, obviously not any, because it's context window is very limited. With a loop and access to an "API" (or willing conversation partner agreeing to act as one) to operate a Turing tape mechanism? It becomes a question of ability to coax it into complying. It trivially has the ability to carry out every step, and your main challenge becomes to get it to stick to it over and over.
One step "up", you can trivially get GPT4 to symbolically solve fairly complex runs of instructions of languages it can never have seen before if you specify a grammar and then give it a program, with the only real limitation again being getting it to continue to adhere to the instructions for long enough before it starts wanting to take shortcuts.
In other words: It can compute any computable function about as well as a reasonably easily distractable/bored human.