xu-2024-gpt4turbo-enumeration-failure

IN premise — summaries/2026/08/24/xu-2024-hallucination-innate-sA-appendix.md

Created 2026-08-24T17:11:30+00:00

GPT-4-turbo (≥175B parameters, 128K context window) fails to enumerate all 7-character strings over the alphabet {a,b} (128 strings, ~896 characters total), demonstrating the failure is computational/logical rather than a memory or context-length limitation.

Summary

Even a tiny combinatorial task — listing all 128 possible 7-character strings of just "a" and "b" — stumps a model with a 128,000-character context window, which rules out simple memory or space constraints. The takeaway is that large language models have a real gap in systematic logical enumeration that no amount of extra context or parameter scale fixes, so any system relying on them for complete combinatorial output needs external verification.