标题： 指定了部分有序集的隐藏理想的有效搜索策略 显示英文标题

标题： An efficient search strategy for hidden ideals in pointed partially ordered sets

摘要： 我们研究了一个组合问题，即在一个已知的带点偏序集 $\lambda$ 中搜索一个未知的理想 $\mu$。可以对 $\lambda$ 的元素进行查询以判断它们是否属于 $\mu$，但最多允许 $k$ 次肯定查询。 我们为该问题提供了一种通用的搜索策略，并基于 $k$ 以及 $\lambda$ 的度数和高度，建立了识别 $\mu$ 所需查询总数的新界限。 我们证明了当高度增长时，该策略在完整的 $\ell$ 元树族上渐近最优。 显示英文摘要

摘要： We consider a combinatorial question about searching for an unknown ideal $\mu$ within a known pointed poset $\lambda$. Elements of $\lambda$ may be queried for membership in $\mu$, but at most $k$ positive queries are permitted. We provide a general search strategy for this problem, and establish new bounds (based on $k$ and the degree and height of $\lambda$) for the total number of queries required to identify $\mu$. We show that this strategy performs asymptotically optimally on the family of complete $\ell$-ary trees as the height grows.