论文标题
Yes-No置换策划者的确切查询复杂性
The Exact Query Complexity of Yes-No Permutation Mastermind
论文作者
论文摘要
策划者是著名的两人游戏。第一个播放器（CodeMaker）选择了第二个播放器（CodeBreaker）应该在最小代码猜测（查询）中破解的秘密代码。因此，Codemaker的职责是通过在每个查询之后提供秘密代码和猜测代码之间明确定义的误差度量来帮助CodeBreaker。我们考虑一个称为Yes-No Ab-Mastermind的变体，其中秘密代码和查询必须不含重复，而Codemaker提供的信息仅表示查询是否完全包含任何正确的位置。对于具有N位置和$ k \ le n $颜色的策划版本，我们证明了$ \ log_2（k+1-n）+\ log_2（k+2-n）+\ dots+\ log_2（k）$的下限和$ n \ log_2（log_2（k）的上限，$ n \ log_2（n \ log_2）（n \ log_2（n）+k $ a $ k $ a BROKE SERUISS BROW ENSUIL INSUILE CHERISE the SERISSURE SERTINE SERTINE SERTINE CODER。对于重要情况$ k = n $，其中秘密代码和查询代表排列，我们的结果暗示着$θ（n \ log_2（n））$查询的确切渐近复杂性。
Mastermind is famous two-players game. The first player (codemaker) chooses a secret code which the second player (codebreaker) is supposed to crack within a minimum number of code guesses (queries). Therefore, codemaker's duty is to help codebreaker by providing a well-defined error measure between the secret code and the guessed code after each query. We consider a variant, called Yes-No AB-Mastermind, where both secret code and queries must be repetition-free and the provided information by codemaker only indicates if a query contains any correct position at all. For this Mastermind version with n positions and $k\le n$ colors we prove a lower bound of $\log_2(k+1-n)+\log_2(k+2-n)+\dots+\log_2(k)$ and an upper bound of $n\log_2(n)+k$ on the number of queries necessary to break the secret code. For the important case $k=n$, where both secret code and queries represent permutations, our results imply an exact asymptotic complexity of $Θ(n\log_2(n))$ queries.
