Author

Xiao-Shan Gao

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Preprint Sep 2026

On the Turing Completeness of Transformers and Agents

It is shown that a single fixed finite precision transformer cannot memorize certain Turing machines with inputs of arbitrary length, such as the arithmetic; and a single fixed infinite precision transformer trained with a random algorithm is not Turing complete with probability one under reasonable conditions.

Y. Qiao, Li-Jia Yu, Rui-Chen Qiu et al. · 0 citations

Preprint Sep 2026

Sparse Polynomial GCD Algorithms Asymptotically Linear in All Fundamental Parameters

This paper presents the first sparse GCD algorithm over the integers that achieves linear complexity in all fundamental parameters simultaneously and is the first sparse GCD algorithm over the integers that achieves linear complexity in all these parameters simultaneously.

Qiao-Long Huang, Xiao-Shan Gao · 0 citations

Preprint Jul 2026

MechMath Agent Team: LLM Driven Agents for Mathematical Research

The MechMath Agent Team (MMAT) is presented, which is a large language model driven agent designed to serve as a co-pilot throughout the full cycle of mathematical research, and a tripartite Harness Architecture that decouples system responsibilities into Control, Execution, and Augmentation planes, thereby reconciling...

Yi-xuan Cao, Ruichen Qiu, Junqi Liu et al. · 3 citations