Position: The Turing-Completeness of Autoregressive Transformers Relies Heavily on Context Management 文章

arXiv:2605.19514v2 Announce Type: replace-cross Abstract: Many works make the eye-catching claim that Transformers are Turing-complete. However, the literature often conflates two distinct settings: (i) a fixed Transformer system setting, in which a fixed autoregressive Transformer is coupled with a fixed context-management method to process inputs of different lengths step by step, and (ii) a scaling-family setting, in which a family of different models (with increasing context-window length or numerical precision) is used to handle different input lengths. Existing proofs of Transformer Turing-completeness are frequently established in setting (ii), whereas real-world LLM deployment and the standard notion of Turing-completeness correspond more naturally to setting (i). In this paper, we first formalize the fixed-system setting, thereby providing a concrete characterization of how real-world LLMs operate.