The Extended Church-Turing Thesis (ECTT) posits that all effective information processing, including unbounded and non-uniform interactive computations, can be described in terms of interactive Turing machines with advice. Does this assertion also apply to the abilities of contemporary large language models (LLMs)? From a broader perspective, this question calls for an investigation of the computational power of LLMs by the classical means of computability and computational complexity theory, especially the theory of automata. Along these lines, we establish a number of fundamental results. Firstly, we argue that any fixed (non-adaptive) LLM is computationally equivalent to a, possibly very large, deterministic finite-state transducer. This characterizes the base level of LLMs. We extend this to a key result concerning the simulation of space-bounded Turing machines by LLMs. Secondly, we show that lineages of evolving LLMs are computationally equivalent to interactive Turing machines with advice. The latter finding confirms the validity of the ECTT for lineages of LLMs. From a computability viewpoint, it also suggests that lineages of LLMs possess super-Turing computational power. Consequently, in our computational model knowledge generation is in general a non-algorithmic process realized by lineages of LLMs. Finally, we discuss the merits of our findings in the broader context of several related disciplines and philosophies.

翻译：扩展的丘奇-图灵论题（ECTT）主张，所有有效的信息处理（包括无界和非均匀的交互式计算）都可以通过带有建议的交互式图灵机来描述。这一论断是否也适用于当代大语言模型（LLMs）的能力？从更广阔的视角来看，这一问题要求通过可计算性和计算复杂性理论（尤其是自动机理论）的经典方法，对LLMs的计算能力进行研究。沿着这一思路，我们建立了若干基本结果。首先，我们论证任何固定（非自适应）的LLM在计算上等价于一个可能非常庞大的确定性有限状态转换器。这刻画了LLMs的基础层级。我们将此扩展为一个关于LLMs模拟空间有界图灵机的关键结果。其次，我们证明进化的LLMs谱系在计算上等价于带有建议的交互式图灵机。后一发现证实了ECTT对于LLMs谱系的有效性。从可计算性的角度来看，这也表明LLMs谱系拥有超图灵计算能力。因此，在我们的计算模型中，知识生成通常是由LLMs谱系实现的非算法过程。最后，我们在多个相关学科和哲学的广阔背景下讨论了这些发现的价值。