LLM will NEVER be AGI: The Proof

2024-08-20

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.