Some Examples of Semi-rational DAG Languages

  • Jan Robert Menzel
  • Lutz Priese
  • Monika Schuth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4036)


The class of semi-rational dag languages can be characterized by labeled Petri nets with ε-transitions, by rather simple leaf substituting tree grammars with additional non-local merge rules, or as a synchronization closure of Courcelles class of recognizable sets of unranked, unordered trees. However, no direct recognition by some magma is known. For a better understanding, we present here some examples of languages within and without the class of semi-rational dag languages.


Terminal State Graph Grammar Tree Automaton Father Node Unordered Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Thomas, W.: Finite-state recognizability of graph properties. In: Krob, D. (ed.) Theorie des Automates et Applications, vol. 172, pp. 147–159. l’Université de Rouen, France (1992)Google Scholar
  2. 2.
    Kamimura, T., Slutzki, G.: Parallel and two-way automata on directed ordered acyclic graphs. Inf. Control 49, 10–51 (1981)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Comon, H., Daucher, M., Gilleron, R., Tison, S., Tommasi, M.: Tree automata techniques and application (1998), available on the Web from in directoty tata
  4. 4.
    Brüggemann-Klein, A., Murata, M., Wood, D.: Regular tree and hedge languages of unranked alphabets. Theor. Comp. Science Center Report HKUST-TCSC 2001-5, 29pages (2001)Google Scholar
  5. 5.
    Courcelle, B.: On recognizable sets and tree automata. In: Aït-Kaci, H., Nivat, M. (eds.) Resolution of Equations in Algebraic Structures, vol. 1, pp. 93–126. Academic Press, London (1989)Google Scholar
  6. 6.
    Priese, L.: Semi-rational Sets of DAGs. In: De Felice, C., Restivo, A. (eds.) DLT 2005. LNCS, vol. 3572, pp. 385–396. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Kreowski, H.J.: A comparison between Petri-nets and graph grammars. In: Noltemeier, H. (ed.) WG 1980. LNCS, vol. 100, pp. 306–317. Springer, Heidelberg (1981)Google Scholar
  8. 8.
    Reisig, W.: A graph grammar representation of nonsequential processes. In: Noltemeier, H. (ed.) WG 1980. LNCS, vol. 100, pp. 318–325. Springer, Heidelberg (1981)Google Scholar
  9. 9.
    Castellani, I., Montanara, H.: Graph grammars for distributed systems. In: Ehrig, H., Nagl, M., Rozenberg, G. (eds.) Graph Grammars 1982. LNCS, vol. 153, pp. 20–38. Springer, Heidelberg (1983)CrossRefGoogle Scholar
  10. 10.
    Genrich, H.J., Janssen, D., Rozenberg, G., Thiagarajan, P.S.: Petri nets and their relation to graph grammars. In: Ehrig, H., Nagl, M., Rozenberg, G. (eds.) Graph Grammars 1982. LNCS, vol. 153, pp. 15–129. Springer, Heidelberg (1983)CrossRefGoogle Scholar
  11. 11.
    Starke, P.: Graph grammars for Petri net processes. EIK 19, 199–233 (1983)MATHMathSciNetGoogle Scholar
  12. 12.
    Grabowski, J.: On partial languages. Annales Societatis Mathematicas Polonae, Fundamenta Informaticae IV.2, 428–498 (1981)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jan Robert Menzel
    • 1
  • Lutz Priese
    • 1
  • Monika Schuth
    • 1
  1. 1.Fachbereich InformatikUniversität Koblenz-LandauGermany

Personalised recommendations