两个缺陷品的自适应定量分组检测的认证精确界
Certified exact bounds for adaptive quantitative group testing with two defectives
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中文总结 AI 辅助
本文确定了在最多k次自适应定量测试下识别两个缺陷品的最大种群规模，给出了八、九、十次测试的精确最大值65、112、192，并提供了显式策略和认证证书。
中文摘要 AI 辅助
我们确定了对于每个$0\le k\le10$，在最多使用$k$次自适应定量测试时，总能识别出恰好两个缺陷品的最大种群规模。每次测试报告所选子集中缺陷品的数量。八次、九次和十次测试的精确最大值分别为65、112和192。我们还对所有包含恰好一个缺陷品的两个不相交集合的大小对进行了分类，这些大小对可以在每个测试预算内通过八次测试解决。这些精确结果由显式策略和最大性证书支持，这些证书由独立于搜索实现的程序检查。其他结果包括部分九次测试边界和针对328个物品的十一次测试策略；后者的最大性仍未解决。
英文摘要
We determine the maximum population size for which exactly two defective items can always be identified using at most $k$ adaptive quantitative tests, for every $0\le k\le10$. Each test reports the number of defectives in a chosen subset. The exact maxima for eight, nine and ten tests are 65, 112 and 192, respectively. We also classify all pairs of sizes of two disjoint sets, each containing exactly one defective, that can be resolved within each test budget through eight. These exact results are supported by explicit strategies and maximality certificates checked by programs separate from the search implementation. Additional results include partial nine-test boundaries and an eleven-test strategy for 328 items; maximality of the latter remains open.
