关于常字母集上的最小同步项
On smallest synchronizing terms over constant alphabets
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中文总结 AI 辅助
该研究针对两符号字母集的确定有限树自动机，证明其重置阈值的次指数级下界，改进了此前二次级下界，缩小了相关指数级下界与上界的差距。
中文摘要 AI 辅助
我们证明了仅含两个符号的字母集上同步确定有限树自动机（DTA）的重置阈值存在次指数级下界，这显著改进了此前与状态数呈二次关系的下界。该结果还缩小了两类下界间的差距：一是随状态数线性增长的字母集上DTA的下界，二是目前已知的最优上界，二者当前均为指数级。
英文摘要
We show a subexponential lower bound on the reset threshold of synchronizing deterministic finite tree automata (DTA) over alphabets of just two symbols. This significantly improves the previous one, which was quadratic in the number of states. Our result also narrows the gap towards the lower bound for DTA over alphabets that grow linearly with the number of states, as well as the best known upper bound, both of which are currently exponential.
发表机构
- TU Dresden（德累斯顿工业大学）
- ScaDS.AI Dresden/Leipzig（萨克森州数据科学与人工智能中心（德累斯顿/莱比锡））
机构由 AI 辅助整理，请以论文原文为准。
