The generative power of delegation networks

A device that generates trees over a ranked alphabet, together with an interpretation of the symbols in that alphabet as functions or relations on some domain, generates subsets of that domain. This well-known concept of tree-based generator is essentially already present in the seminal paper by Mezei and Wright from 1967. A delegation network consists of a finite set of such generators that can “delegate” parts of the generation process to each other. It can be viewed as an (extended) IO context-free tree grammar with an interpretation. We investigate the theoretical properties of these networks and establish several characterizations of the generated subsets, in the style of Mezei and Wright. We also show that the hierarchy of tree language classes obtained by iterating the concept of delegation, is properly contained in the closure of the regular tree languages under nondeterministic macro tree transductions, but not contained in the IO-hierarchy.