带假设的决策树用于单调布尔函数的识别和排序
Decision Trees with Hypotheses for Recognition of Monotone Boolean Functions and for Sorting
摘要：
在本文中，我们考虑决策树，使用查询的基础上的一个属性，每个和查询的假设的所有属性的值。这种决策树类似于精确学习中研究的决策树，其中不仅允许成员资格，而且允许等价查询。研究了以$n$为变量的单调布尔函数$n=2, \ldots, 4$的识别问题，以及从线性序集$n=3, \ldots, 6$中对$n$两两不同元素进行排序的问题.对于这些问题中的每一个，我们比较了不同类型的最优（相对于深度或可实现节点的数量）决策树与假设的复杂性。我们还研究了基于熵的贪心算法构造的决策树的复杂性，并分析了从这些树中得到的决策规则的长度。
英文摘要：
In this paper, we consider decision trees that use both queries based on one attribute each and queries based on hypotheses about values of all attributes. Such decision trees are similar to ones studied in exact learning, where not only membership but also equivalence queries are allowed. We investigate the problem of recognition of monotone Boolean functions with $n$ variables, $n=2, \ldots, 4$, and the problem of sorting $n$ pairwise different elements from linearly ordered set, $n=3, \ldots, 6$. For each of these problems, we compare the complexity of different types of optimal (relative to the depth or the number of realizable nodes) decision trees with hypotheses. We also study the complexity of decision trees constructed by entropy-based greedy algorithm and analyze the length of decision rules derived from these trees.
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。
