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Preprint Oct 2026

From Events to Reasoning: Hierarchical Rule Composition over Explicit States

What a reasoning system emits is a conclusion; what it owes is a justification. Producing one requires every operation to be admissible on the facts actually available, the dependencies of intermediate results to survive to the end of the path, and the path to be revised when a premise changes. We present the Event Rea...

Cheng Lyu, Xue-Qi Wang · 0 citations
Preprint Sep 2026

A Class of Shift-Invariant Permutations and Their Algebraic Structure

Shift-invariant permutations of $\mathbb F_2^n$ are attractive in symmetric cryptography because of their regularity and implementation efficiency. Constructing such permutations with an explicit algebraic structure remains a challenging problem. In this paper, we study a family of shift-invariant transformations of $\...

Cheng Lyu, Da-Bin Zheng, Yu-Cen Mu et al. · 0 citations

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