Sure; but an LLM can do all those things too. We're talking about a very restricted problem domain with clear deterministic inputs and outputs, neural nets outp

Sure; but an LLM can do all those things too. We're talking about a very restricted problem domain with clear deterministic inputs and outputs, neural nets outperform humans under those conditions. Any computer-based method can. So if we take as a starting point that LLMs can't simulate Turing machines and that is important, the tasks you are referring to won't involve simulating Turing machines either. I personally suspect LLMs can simulate Turing machines. Turing machines are pretty basic. Particularly after noting that humans use external tools like pen & paper, so it'd be fair to train the LLM to use some external memory-aiding tool. Then it becomes an academically trivial problem for even a basic neural net.