In the realm of machine learning theory, to prevent unnatural coding schemes between teacher and learner, No-Clash Teaching Dimension was introduced as provably optimal complexity measure for collusion-free teaching. However, whether No-Clash Teaching Dimension is upper-bounded by Vapnik-Chervonenkis dimension remains unknown. In this paper, for any finite concept class, we construct fragments of size equals to its Vapnik-Chervonenkis dimension which identify concepts through an ordered compression scheme. Naturally, these fragments are used as teaching sets, one can easily see that they satisfy the non-clashing condition, i.e., this open question is resolved for finite concept classes.

翻译：在机器学习理论领域，为消除教师与学习者之间非自然的编码方案，无冲突教学维度被提出作为免串通教学的最优复杂度度量。然而，无冲突教学维度是否受Vapnik-Chervonenkis维数上界约束这一问题仍悬而未决。本文针对任意有限概念类，构造了规模等于其Vapnik-Chervonenkis维数的片段，这些片段通过有序压缩方案识别概念。自然而言，将这些片段作为教学集时，可直观验证其满足无冲突条件——即本开放问题对有限概念类得以解决。