What are examples for XOR, parity and multiplexer problems in decision tree learning?
Below is an example of XOR dataset for classification. As you can see, decision trees perform pretty poorly on this dataset. Reason is decision trees splits space into rectangular regions. Therefore they are not pretty good with this kind of distributions.

If you really want to use trees in that sort of situation, it is interesting to use so-called rotation trees. Rotation is about performing PCA (principal components analysis) on input features while learning trees. Using it, decision trees can then build non-rectangular regions.



Also, here is a playground to test gradient boosting algorithms including on XOR dataset. It is really interesting ! You can click on "rotate trees" to activate rotation.
Gradient boosting playground