偏序集上流沙理想的搜索
Searching for quicksand ideals in partially ordered sets
摘要：
我们考虑一个组合问题，寻找一个未知的理想$μ$内的一个已知偏序集$λ$。可以查询$λ$的元素以获得$μ$中的成员资格，但最多允许$k$肯定的查询结果。我们的目标是找到一个搜索策略，保证在最小的总查询数$m_k(λ)$的解决方案。给出了$m_k(λ)$的紧界，并对$k=2$和$λ$是全序有限集的乘积偏序集，且其中一个偏序集的基数不超过6的情形构造了最优搜索策略.
英文摘要：
We consider a combinatorial question about searching for an unknown ideal $μ$ within a known poset $λ$. Elements of $λ$ may be queried for membership in $μ$, but at most $k$ positive query results are permitted. The goal is to find a search strategy which guarantees a solution in a minimal total number $m_k(λ)$ of queries. We provide tight bounds for $m_k(λ)$, and construct optimal search strategies for the case where $k=2$ and $λ$ is the product poset of totally ordered finite sets, one of which has cardinality not more than six.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
