关于三个相同伪硬币问题的一些新结果

Some New Results Concerning Three Uniform Defective Coins Problem

本文中,给定一台比较型测试装置和确切的三个相同伪硬币出现的信息,作者研究最小测试数的探求问题,这个最小测试数能从λ个有同样外观的硬币组成的集合中鉴别出三个相同的伪硬币,这里λ≥4.作者构造了对于无限多个λ值的一个最优鉴别分组测试算法,这个最优鉴别分组测试算法改进了Toic的对于无限多个λ值的一个最优鉴别分组测试算法,也改进了Bonjak的对于无限多个λ值的一个最优鉴别分组测试算法.作者还提出另一个鉴别分组测试算法,并且猜想这个算法是最优的.

In this paper authors consider the problem of ascertaining the minimum number of testings suffice to identify the three defective coins of uniform weight in a set ofλ, coins of the same appearance, given a comparison-type device and the information that there are exactly the three defective coins of uniform present,where）, λ ≥4. An optimal testing algorithm is constructed for infinitely many）λ＇s . The optimal testing algorithm has improved the optimal testing algorithm of Togic for infinitel manyλ＇s ,and the optimal testing algorithm of Bognjak for infintely manyλ＇s . The other testing algorithm is still proposed,and it is conjectured that the algorithm is optimal.