HASSE diagrams for classes of deterministic bottom-up tree-to-tree-series transformations

The relationship between classes of tree-to-tree-series and o-tree-to-tree-series transformations, which are computed by restricted deterministic bottom-up weighted tree transducers, is investigated. Essentially, these transducers are deterministic bottom-up tree series transducers, except that the former are defined over monoids whereas the latter are defined over semirings and only use the multiplicative monoid thereof. In particular, the common restrictions of nondeletion, linearity, totality, and homomorphism can equivalently be defined for deterministic bottom-up weighted tree transducers. Using well-known results of classical tree transducer theory and also new results on deterministic weighted tree transducers, classes of tree-to-tree-series and o-tree-to-tree-series transformations computed by restricted deterministic bottomup weighted tree transducers are ordered by set inclusion. More precisely, for every commutative monoid and all sensible combinations of the above mentioned restrictions, the inclusion relation of the classes of tree-to-tree-series and o-tree-to-treeseries transformations is completely conveyed by means of Hasse diagrams.