We study a model of machine teaching where the teacher mapping is constructed from a size function on both concepts and examples. The main question in machine teaching is the minimum number of examples needed for any concept, the so-called teaching dimension. A recent paper [7] conjectured that the worst case for this model, as a function of the size of the concept class, occurs when the consistency matrix contains the binary representations of numbers from zero and up. In this paper we prove their conjecture. The result can be seen as a generalization of a theorem resolving the edge isoperimetry problem for hypercubes [12], and our proof is based on a lemma of [10].

翻译：我们研究了一种机器教学模型，其中教师映射是基于概念和示例上的规模函数构建的。机器教学中的核心问题是任何概念所需的最小示例数量，即所谓的教学维度。近期的一篇论文[7]推测，在该模型中，作为概念类规模函数的最坏情况发生在当一致性矩阵包含从零开始递增的数字的二进制表示时。本文我们证明了这一猜想。该结果可视为超立方体边等周问题定理[12]的一种推广，我们的证明基于文献[10]中的引理。