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Quasi-Perfect Minimally Adaptive q-ary Search with Unreliable Tests

机译:Quasi-Perfice最新自适应Q-Ary搜索,具有不可靠的测试

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We consider the problem of determining the minimum number of queries to find an unknown number in a finite set when up to a finite number e. of the answers may be erroneous. In the vast literature regarding this problem, the classical case of binary search is mostly considered, that is, when only yes-no questions are allowed. In this paper we consider the variant of the problem in which questions with q many possible answers are allowed. We prove that at most one question more than the information theoretic lower bound is sufficient to successfully find the unknown number. Moreover we prove that there are infinitely many cases when the information theoretic lower bound is exactly attained and the so called perfect, strategies exist. Our strategies have the important feature that they use a minimum amount of adaptiveness, a relevant property in many practical situation.
机译:我们考虑确定在UNITE e的有限集中找到未知数量的最小查询数量的问题。答案可能是错误的。在关于这个问题的广泛文献中,大多数考虑了二进制搜索的经典案例,即,只允许yes-否问​​题。在本文中,我们考虑了问题的变体,其中允许Q有许多可能的答案。我们证明,大多数问题超过信息,理论下限足以成功找到未知数字。此外,我们证明了无数情况下,当信息理论下限完全达到了信息,所谓的完美,策略存在。我们的策略具有他们在许多实际情况下使用最低适应性的重要特点。

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