On the depth of decision trees over infinite 1-homogeneous binary information systems

In this paper, we study decision trees, which solve problems defined over a specific subclass of infinite information systems, namely: 1-homogeneous binary systems. It is proved that the minimum depth tree (defined as function on number attributes in problem’s description) grows – worst case logarithmically or linearly for each system class. We consider examples including one closely related to trees constructed by CART algorithm.