Equational weighted tree transformations
The authors consider polynomial systems of equations of weighted term relations over commutative continuous semirings. A weighted relation between two algebras is called equational if it is a component of the least solution of such a system. This least solution is obtained as the least fixed point of an \(\omega\)-continuous operator. Equational weighted tree transformations are the equational weighted relations between two term algebras. The equational weighted tree transformations, as well as some special types of them, are characterized in terms of weighted tree bimorphisms, i.e., systems consisting of two tree homomorphisms and a recognizable weighted tree language. Furthermore, the weighted tree transformations computed by weighted linear nondeleting tree transducers and weighted linear nondeleting extended tree transducers are given equational characterizations. Finally, the authors present a Mezei-Wright like result showing that the weighted equational relations between any two algebras are the images of a certain kind of weighted equational tree transformations.
scientific article; zbMATH DE number 6018102
scientific article