A Characterization of the Sets of Hypertrees Generated by Hyperedge-Replacement Graph Grammars

A characterization of the languages of hypertrees generated by hyperedge-replacement graph grammars is established. The characterization says that these languages are exactly those described by sets of derivation trees which are output languages of finite-copying top-down tree transducers. Furthermore, the statement remains valid if the tree transducers are required to generate derivation trees in which the right-hand sides of productions are hypertrees and the nonterminal hyperedges are at most as large as the hyperedges in the generated hypertrees. This result is closely related to a similar characterization that was obtained for the case of string graphs by Engelfriet and Heyker some years ago. In fact, the results of this paper also yield a new proof for the characterization by Engelfriet and Heyker. Received August 1997, and in final form May 1998.