发表机构
University of Toronto Scarborough（多伦多大学士嘉堡校区）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该论文构造了强连通双字母同步自动机，证明其三重会合时间可达 floor(4n/3)，并给出下界证明与显式词。
AI 中文摘要
对于每个 $n\ge9$，我们构造了一个强连通的双输入字母同步自动机，具有 $n$ 个状态，其合并三个不同状态的最短词的长度为 $\lfloor4n/3\rfloor$。其中一个字母是置换；另一个字母的像的大小为 $n-1$。我们给出了完整的转移映射和一个达到该界限的显式词。对于下界，我们为每个无序状态对分配一个整数，并证明应用任一输入字母最多能使其减少一。对于 $n\not\equiv0\pmod3$，相同的构造包含一个指定状态，其与自由选择的伙伴合并的最短词的长度为 $\lfloor4n/3\rfloor-1$。
英文摘要
For every $n\ge9$, we construct a strongly connected synchronizing automaton with two input letters and $n$ states whose shortest word merging some three distinct states has length $\lfloor4n/3\rfloor$. One letter is a permutation; the other has an image of size $n-1$. We give complete transition maps and an explicit word attaining the bound. For the lower bound, we assign an integer to each unordered pair of states and prove that applying either input letter can decrease it by at most one. For $n\not\equiv0\pmod3$, the same construction contains a specified state whose shortest merging word, with its partner chosen freely, has length $\lfloor4n/3\rfloor-1$.
Comments42 pages, including additional results and computational notes. Computational data are available at https://doi.org/10.5281/zenodo.22561629
