The Equivalence of Bottom-Up and Top-Down Tree-to-Graph Transducers

The Equivalence of Bottom-Up and Top-Down Tree-to-Graph Transducers

We introduce the bottom-up tree-to-graph transducer, which is very similar to the usual (total deterministic) bottom-up tree transducer except that it translates trees into hypergraphs rather than trees, using hypergraph substitution instead of tree substitution. If every output hypergraph of the transducer is a jungle, i.e., a hypergraph that can be unfolded into a tree, then the tree-to-graph...

Top-Down Tree-To-Graph Transducers

We introduce a new syntax-directed translation device called top-down treeto-graph transducer. Such transducers are very similar to the usual top-down tree trans ducers except that the right-hand sides of their rules are hypergraphs rather than trees. Since we are aiming at a device which also allows to translate trees into objects ditTerent from graphs, we focus our attention on so-called tree...

The Translation Power of Top-Down Tree-to-Graph Transducers

We introduce a new syntax-directed translation device called top-down tree-to-graph transducer. Such transducers are very similar to the usual (total deterministic) top-down tree transducers except that the right-hand sides of their rules are hypergraphs rather than trees. Since we are aiming at a device which also allows us to translate trees into objects different from graphs, we focus our at...

Bottom-up, top-down

Bottom-Up and Top-Down Tree Series Transformations

We generalize bottom-up tree transducers and top-down tree transducers to the concept of bottom-up tree series transducer and top-down tree series transducer, respectively, by allowing formal tree series as output rather than trees, where a formal tree series is a mapping from output trees to some semiring. We associate two semantics with a tree series transducer: a mapping which transforms tre...