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:2502.17779 , year=
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For any ρ>0 there exists a ρ-TV-stable RL algorithm for tabular MDPs supporting exact unlearning at expected cost ρ√(ln T) of retraining from scratch, with regret O(H²√(SAT)+H³S²A+H^{2.5}S²A/ρ) and matching lower bound Ω(H√(SAT)+SAH/ρ).
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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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Exact Unlearning in Reinforcement Learning
For any ρ>0 there exists a ρ-TV-stable RL algorithm for tabular MDPs supporting exact unlearning at expected cost ρ√(ln T) of retraining from scratch, with regret O(H²√(SAT)+H³S²A+H^{2.5}S²A/ρ) and matching lower bound Ω(H√(SAT)+SAH/ρ).