Compositions with superlinear deterministic top-down tree transformations

AbstractWe denote the class of deterministic top-down tree transformations by DT and the class of homomorphism tree transformations by HOM. The sign of a class with the prefix l- (sl-, nd-) denotes the linear (superlinear, nondeleting) subclass of that class. We fix the set M = HOM,sl-DT, l-DT, nd-DT, DT of tree transformation classes. Then consider the monoid [M] of all tree transformation classes of the form X1 O … OXm, where O is the operation composition, m ⩾ 0 and the Xi's are elements of M. As the main result of the paper, we give an effective description of the monoid [M] with respect to inclusion. This means that we present an algorithm which can decide, given arbitrary two elements of the monoid, whether some inclusion, equality or incomparability holds between them