arXiv:2507.07505v1 Announce Type: cross Abstract: With widespread adoption of transformer-based language models in AI, there is significant interest in the limits of LLMs capabilities, specifically so-called hallucinations, occurrences in which LLMs provide spurious, factually incorrect or nonsensical information when prompted on certain subjects. Furthermore, there is growing interest in agentic uses of LLMs - that is, using LLMs to create agents that act autonomously or semi-autonomously to carry out various tasks, including tasks with applications in the real world. This makes it important to understand the types of tasks LLMs can and cannot perform. We explore this topic from the perspective of the computational complexity of LLM inference. We show that LLMs are incapable of carrying out computational and agentic tasks beyond a certain complexity, and further that LLMs are incapable of verifying the accuracy of tasks beyond a certain complexity. We present examples of both, then discuss some consequences of this work.