Learning k-Testable tree sets from positive data*

A k-Testable tree set in the Strict sense (k-TS) is essentially defined by a finite set of patterns of "size" k that are permitted to appear in the trees of the tree language. Given a positive sample S of trees over a ranked alphabet, an algorithm is proposed which obtains the smallest k-TS tree set containing S. The proposed algorithm is polynomial on the size of S and identifies the class of k-TS tree languages in the limit from positive data.