Sliding-window transformers without positional encodings are Turing complete because the sliding window breaks permutation symmetry and suffices to simulate Post machines via a constant-size histogram state.
arXiv preprint arXiv:2506.12027 , year=
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LLMs display clear performance stratification on formal language tasks aligned with Chomsky hierarchy complexity levels, limited by severe efficiency barriers rather than absolute capability.
citing papers explorer
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Rethinking the Role of Positional Encoding: Sliding-Window Transformers without PE Remain Turing Complete
Sliding-window transformers without positional encodings are Turing complete because the sliding window breaks permutation symmetry and suffices to simulate Post machines via a constant-size histogram state.
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Evaluating the Formal Reasoning Capabilities of Large Language Models through Chomsky Hierarchy
LLMs display clear performance stratification on formal language tasks aligned with Chomsky hierarchy complexity levels, limited by severe efficiency barriers rather than absolute capability.