Suspect this is a troll posting, but on the off chance I'm wrong... The LLM gives the output of a command. To do so, it has to be able to determine when the command exits. This is exactly the halting problem.
For a trivial example, what is the output of:
```
while True:
pass
print("goodby world")
```
(this is also proof that leaving out the curly braces makes code harder instead of simpler #python-lie-to-me. multiple edits to get this to render correctly on HN )
Rice's theorem may actually be more appropriate here (but it's a consequence of the halting theorem).
But it's important to note that just because there's no algorithm that works on ALL programs doesn't mean that the semantic properties of all programs are undecidable. Clearly for the particular programs where the program is bounded and guaranteed to terminate (e.g. no unbounded loops or recursion allowed) we can determine such properties, and I believe theorem provers in fact only allow such programs. And similarly you can restrict yourself to only the programs that you can prove will terminate in N steps (which might be excluding some programs that do terminate but require more than N steps of compute to prove).
For a trivial example, what is the output of:
```
while True:
print("goodby world") ```(this is also proof that leaving out the curly braces makes code harder instead of simpler #python-lie-to-me. multiple edits to get this to render correctly on HN )