The only computations that an LLM does are backprops and forward passes. It can not run any arbitrary program description. Yes, it will hallucinate your program's output if you feed it some good enough starting prompt. But that's it.
I was not clear enough, thanks. Whether it is a pok or zk depends on the chosen signature scheme. In any case, zk signature schemes exist and are implied by the existence of one way functions and publicly verifiable nizk