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Chen Xu

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Preprint Oct 2026

An Improved Lower Bound for Separating Words by Permutation Automata

We prove that some pairs of binary words of every sufficiently large prescribed length $n$ require $\Omega(\log n\log\log n)$ states to separate by a deterministic finite automaton whose letters act as permutations. We obtain this bound by constructing distinct equal-length positive binary words that form an identity o...

Chen Xu, K. Regan · 0 citations
Preprint Sep 2026

An Elementary Proof of the $\widetilde O(n^{1/3})$ Bound for Separating Words

For two distinct binary words of length $n$, the separating words problem asks for a small deterministic finite automaton that accepts exactly one of them. Chase proved a $\widetilde O(n^{1/3})$ upper bound using a complex-analytic estimate for sparse polynomials. We replace that estimate by a finite-difference argumen...

Chen Xu · 0 citations
Conference Aug 2026

Batch Weight-Averaged Broad Learning System for Improved Generalization

The Broad Learning System (BLS) enables efficient closed-form training by solving the output weights in a single ridge-regression step. However, this one-shot full-batch estimator often exhibits a pronounced generalization gap. This paper proposes Batch Weight-Averaged BLS (BWA-BLS), which partitions the training set i...

Chen Xu · 0 citations

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