Advertisement

Approximating Parikh Images for Generating Deterministic Graph Parsers

  • Frank Drewes
  • Berthold Hoffmann
  • Mark Minas
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9946)

Abstract

The Parikh image of a word abstracts from the order of its letters. Parikh’s famous theorem states that the set of Parikh images of a context-free string language forms a semilinear set that can be effectively computed from its grammar. In this paper we study the computation of Parikh images for graph grammars defined by contextual hyperedge replacement (CHR). Our motivation is to generate efficient predictive top-down (PTD) parsers for a subclass of CHR grammars. We illustrate this by describing the subtask that identifies the nodes of the input graph that parsing starts with.

Keywords

Input Graph Derivation Tree Grammar Graph Start Node Terminal Symbol 
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.

Notes

Acknowledgements

We thank the anonymous reviewers for the valuable comments.

References

  1. 1.
    Brzozowski, J.A.: Derivatives of regular expressions. J. ACM 11(4), 481–494 (1964)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Costagliola, G., Chang, S.K.: Using linear positional grammars for the LR parsing of 2-D symbolic languages. Grammars 2(1), 1–34 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Drewes, F., Hoffmann, B.: Contextual hyperedge replacement. Acta Informatica 52(6), 497–524 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Drewes, F., Hoffmann, B., Minas, M.: Predictive top-down parsing for hyperedge replacement grammars. In: Parisi-Presicce, F., Westfechtel, B. (eds.) ICGT 2015. LNCS, vol. 9151, pp. 19–34. Springer, Heidelberg (2015). doi: 10.1007/978-3-319-21145-9_2 CrossRefGoogle Scholar
  5. 5.
    Esparza, J., Kiefer, S., Luttenberger, M.: Newton’s method for \(Omega\)-continuous semirings. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008. LNCS, vol. 5126, pp. 14–26. Springer, Heidelberg (2008). doi: 10.1007/978-3-540-70583-3_2 CrossRefGoogle Scholar
  6. 6.
    Fischer, P.C., Meyer, A.R., Rosenberg, A.L.: Counter machines and counter languages. Math. Syst. Theor. 2, 265–283 (1968)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Franck, R.: A class of linearly parsable graph grammars. Acta Informatica 10(2), 175–201 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Huynh, T.-D.: The complexity of semilinear sets. In: Bakker, J., Leeuwen, J. (eds.) ICALP 1980. LNCS, vol. 85, pp. 324–337. Springer, Heidelberg (1980). doi: 10.1007/3-540-10003-2_81 CrossRefGoogle Scholar
  9. 9.
    Ibarra, O.H., Seki, S.: Characterizations of bounded semilinear languages by one-way and two-way deterministic machines. Int. J. Found. Comput. Sci. 23(6), 1291–1305 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Kaul, M.: Practical applications of precedence graph grammars. In: Ehrig, H., Nagl, M., Rozenberg, G., Rosenfeld, A. (eds.) Graph Grammars 1986. LNCS, vol. 291, pp. 326–342. Springer, Heidelberg (1987). doi: 10.1007/3-540-18771-5_62 CrossRefGoogle Scholar
  11. 11.
    Lavado, G.J., Pighizzini, G., Seki, S.: Converting nondeterministic automata and context-free grammars into Parikh equivalent deterministic automata. In: Yen, H.-C., Ibarra, O.H. (eds.) DLT 2012. LNCS, vol. 7410, pp. 284–295. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-31653-1_26 CrossRefGoogle Scholar
  12. 12.
    Parikh, R.J.: On context-free languages. J. ACM 13(4), 570–581 (1966)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    To, A.W.: Model checking infinite-state systems: generic and specific approaches. Ph.D. thesis, School of Informatics, University of Edinburgh, August 2010Google Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Umeå UniversitetUmeåSweden
  2. 2.Universität BremenBremenGermany
  3. 3.Universität der Bundeswehr MünchenNeubibergGermany

Personalised recommendations