The proof is trivial with a little help of a necessary condition of complexity theories. All LLM runs under the complexity of $O(n)$, where $n$ is the length of the output.

Suppose LLM is AGI, then it is able to solve any problem that a human can solve. Consider the following problem:

Given a string $s$ of length $n$, determine whether $s$ is a palindrome. Answer “Y” if it is and “N” if it isn’t.

Apprently, a human can solve this problem, and it is easy to prove that the problem must be solved in at least $O(n)$ time.

Since the output of this problem is of a constant length, LLM must solve this problem in $O(1)$ time, which is a contradiction. Thus LLM cannot solve a problem that a human can solve. Therefore LLM is not AGI. $\blacksquare$

EDIT: Chain of Thoughts breaks the proof, allowing LLM to solve the problem in arbitrary time.

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