On the generation of trees by hyperedge replacement
A characterization of the sets of hypertrees generated by hyperedge-replacement graph grammars is established. It says that these sets are exactly those of the form val(T), where T, a set of terms over hyperedge-replacement operations, is the output language of a finite-copying top-down tree transducer. Furthermore, the terms in T may be required to consist of hyperedge-replacement operations whose underlying hypergraphs are hypertrees. The 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.
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- [DHK97]Frank Drewes, Annegret Habel, and Hans-Jörg Kreowski. Hyperedge replacement graph grammars. In G. Rozenberg, editor, Handbook of Graph Grammars and Computing by Graph Transformations. Vol. I: Foundations, chapter 2, pages 95–162. World Scientific, 1997.Google Scholar
- [Dre97]Frank Drewes. A characterization of the sets of hypertrees generated by hyperedge-replacement graph grammars. Report 3/97, Univ. Bremen, 1997.Google Scholar
- [Eng97]Joost Engelfriet. Context-free graph grammars. In G. Rozenberg and A. Salomaa, editors, Handbook of Formal Languages. Vol. III: Beyond Words, chapter 3, pages 125–213. Springer, 1997.Google Scholar
- [GS97]Ferenc Gécseg and Magnus Steinby. Tree languages. In G. Rozenberg and A. Salomaa, editors, Handbook of Formal Languages. Vol. III: Beyond Words, chapter 1, pages 1–68. Springer, 1997.Google Scholar
- [Hab92]Annegret Habel. Hyperedge Replacement: Grammars and Languages, volume 643 of Lecture Notes in Computer Science. Springer-Verlag, 1992.Google Scholar