Tree Languages Generated by Context-Free Graph Grammars

  • Joost Engelfriet
  • Sebastian Maneth
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1764)


A characterization is given of the class of tree languages which can be generated by context-free hyperedge replacement (HR) graph grammars, in terms of macro tree transducers (MTTs). This characterization yields a normal form for tree generating HR graph grammars. Moreover, two natural, structured ways of generating trees with HR graph grammars are considered and an inclusion diagram of the corresponding classes of tree languages is proved. Finally, the MSO definable tree transductions are characterized in terms of MTTs.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. AD76.
    Arnold, A., Dauchet, M.: Un théorème de duplication pour les forêts algébriques. J. of Comp. Syst. Sci. 13, 223–244 (1976)zbMATHMathSciNetCrossRefGoogle Scholar
  2. AU71.
    Aho, A.V., Ullman, J.D.: Translations on a context-free grammar. Inform. and Control 19, 439–475 (1971)CrossRefMathSciNetGoogle Scholar
  3. BC87.
    Bauderon, M., Courcelle, B.: Graph expressions and graph rewritings. Math. Systems Theory 20, 83–127 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  4. BE98.
    Bloem, R., Engelfriet, J.: A comparison of tree transductions defined by monadic second order logic and by attribute grammars. Technical Report 98-02, Leiden University (1998); To appear in J. of Comp. Syst. Sci. Google Scholar
  5. CE95.
    Courcelle, B., Engelfriet, J.: A logical characterization of the sets of hypergraphs defined by hyperedge replacement grammars. Math. Systems Theory 28, 515–552 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  6. CF82.
    Courcelle, P., Franchi-Zannettacci, P.: Attribute grammars and recursive program schemes. Theoret. Comput. Sci. 17, 163–191 and 235–257 (1982)Google Scholar
  7. Cou90.
    Courcelle, B.: The monadic second-order logic of graphs. I. recognizable sets of infinite graphs. Information and Computation 85, 12–75 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  8. Cou94.
    Courcelle, B.: Monadic second-order definable graph transductions: a survey. Theoret. Comput. Sci. 126, 53–75 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  9. DKH97.
    Drewes, F., Kreowski, H.-J., Habel, A.: Hyperedge replacement graph grammars. In: Rozenberg, G. (ed.) Handbook of Graph Grammars and computing by graph transformation, ch. 2, vol. 1, pp. 95–162. World Scientific, Singapore (1997)CrossRefGoogle Scholar
  10. DPSS77.
    Duske, J., Parchmann, R., Sedello, M., Specht, J.: IO-macrolanguages and attributed translations. Inform. and Control 35, 87–105 (1977)CrossRefMathSciNetGoogle Scholar
  11. Dre96.
    Drewes, F.: Computation by Tree Transductions. PhD thesis, University of Bremen (1996) Google Scholar
  12. Dre99.
    Drewes, F.: A characterization of the sets of hypertrees generated by hyperedge-replacement graph grammars. Theory Comput. Systems 32, 159–208 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  13. EF81.
    Engelfriet, J., Filè, G.: The formal power of one-visit attribute grammars. Acta Informatica 16, 275–302 (1981)zbMATHCrossRefMathSciNetGoogle Scholar
  14. EH92.
    Engelfriet, J., Heyker, L.: Context-free hypergraph grammars have the same term-generating power as attribute grammars. Acta Informatica 29, 161–210 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  15. EM98.
    Engelfriet, J., Maneth, S.: Macro tree transducers, attribute grammars, and MSO definable tree translations. Technical Report 98-09, Leiden University (1998) ; To appear in Inform. and Comput. Google Scholar
  16. Eng94.
    Engelfriet, J.: Graph grammars and tree transducers. In: Tison, S. (ed.) CAAP 1994. LNCS, vol. 787, pp. 15–36. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  17. Eng97.
    Engelfriet, J.: Context-free graph grammars. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, ch. 3, vol. 3. Springer, Heidelberg (1997)Google Scholar
  18. ERS80.
    Engelfriet, J., Rozenberg, G., Slutzki, G.: Tree transducers, L systems, and two-way machines. J. of Comp. Syst. Sci. 20, 150–202 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  19. ES77.
    Engelfriet, J., Schmidt, E.M.: IO and OI, Part I. J. of Comp. Syst. Sci. 15, 328–353 (1977); And Part II, J. of Comp. Syst. Sci. 16, 67–99 (1978) zbMATHCrossRefMathSciNetGoogle Scholar
  20. EV85.
    Engelfriet, J., Vogler, H.: Macro tree transducers. J. of Comp. Syst. Sci. 31, 71–146 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  21. FV98.
    Fülöp, Z., Vogler, H.: Syntax-Directed Semantics – Formal Models based on Tree Transducers. In: Brauer, W., Rozenberg, G., Salomaa, A. (eds.) EATCS Monographs on Theoretical Computer Science. Springer, Heidelberg (1998)Google Scholar
  22. GS84.
    Gécseg, F., Steinby, M.: Tree Automata. Akadémiai Kiadó, Budapest (1984)zbMATHGoogle Scholar
  23. GS97.
    Gécseg, F., Steinby, M.: Tree automata. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, ch. 1, vol. 3. Springer, Heidelberg (1997)Google Scholar
  24. Hab89.
    Habel, A.: Hyperedge Replacement: Grammars and Languages. PhD thesis, University of Bremen (1989) Google Scholar
  25. Hab92.
    Habel, A.: Hyperedge Replacement: Grammars and Languages. LNCS, vol. 643. Springer, Heidelberg (1992)zbMATHGoogle Scholar
  26. Man98.
    Maneth, S.: The generating power of total deterministic tree transducers. Inform. and Comput. 147, 111–144 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  27. Plu98.
    Plump, D.: Term graph rewriting. Technical Report CSI-R9822, Computing Science Institute Nijmegen (1998); To appear in Handbook of Graph Grammars and Computing by Graph Transformation, vol. 2. World Scientific, Singapore Google Scholar
  28. Rao97.
    Raoult, J.-C.: Rational tree relations. Bull. Belg. Math. Soc. 4, 149–176 (1997)zbMATHMathSciNetGoogle Scholar
  29. Rou70.
    Rounds, W.C.: Mappings and grammars on trees. Math. Systems Theory 4, 257–287 (1970)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Joost Engelfriet
    • 1
  • Sebastian Maneth
    • 1
  1. 1.LIACSLeiden UniversityLeidenThe Netherlands

Personalised recommendations