Tree Automata and XPath on Compressed Trees

  • Markus Lohrey
  • Sebastian Maneth
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3845)


The complexity of various membership problems for tree automata on compressed trees is analyzed. Two compressed representations are considered: dags, which allow to share identical subtrees in a tree, and straight-line context-free tree grammars, which moreover allow to share identical intermediate parts of a tree. Several completeness results for the classes NL, P, and PSPACE are obtained. Finally, the complexity of the XPath evaluation problem on trees that are compressed via straight-line context-free tree grammars is investigated.


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  1. 1.
    Lohrey, M.: Word problems on compressed word. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 906–918. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  2. 2.
    Rytter, W.: Grammar compression, LZ-encodings, and string algorithms with implicit input. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 15–27. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  3. 3.
    Plump, D.: Term graph rewriting. In: Ehrig, H., Engels, G., Kreowski, H.J., Rozenberg, G. (eds.) Handbook of Graph Grammars and Computing by Graph Transformation, vol. 2, pp. 3–61. World Scientific, Singapore (1999)CrossRefGoogle Scholar
  4. 4.
    Bryant, R.E.: Symbolic boolean manipulation with ordered binary-decision diagrams. ACM Computing Surveys 24, 293–318 (1992)CrossRefGoogle Scholar
  5. 5.
    Buneman, P., Grohe, M., Koch, C.: Path queries on compressed XML. In: Freytag, J.C., et al. (eds.) Proc. VLDB 2003, pp. 141–152. Morgan Kaufmann, San Francisco (2003)CrossRefGoogle Scholar
  6. 6.
    Frick, M., Grohe, M., Koch, C.: Query evaluation on compressed trees (extended abstract). In: Proc. LICS 2003, pp. 188–197. IEEE Computer Society Press, Los Alamitos (2003)Google Scholar
  7. 7.
    Maneth, S., Busatto, G.: Tree transducers and tree compressions. In: Walukiewicz, I. (ed.) FOSSACS 2004. LNCS, vol. 2987, pp. 363–377. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  8. 8.
    Comon, H., Dauchet, M., Gilleron, R., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree automata techniques and applications (2002), available on:
  9. 9.
    Busatto, G., Lohrey, M., Maneth, S.: Efficient memory representation of XML documents. In: Bierman, G., Koch, C. (eds.) DBPL 2005. LNCS, vol. 3774, Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Gécseg, F., Steinby, M.: Tree automata. Akadémiai Kiadó (1984)Google Scholar
  11. 11.
    Murata, M., Lee, D., Mani, M.: Taxonomy of XML Schema Languages using Formal Language Theory. In: Proc. Extreme Markup Languages 2000, Montréal (Canada) (2000)Google Scholar
  12. 12.
    Neven, F.: Automata theory for XML researchers. SIGMOD Record 31, 39–46 (2002)CrossRefGoogle Scholar
  13. 13.
    Lohrey, M.: On the parallel complexity of tree automata. In: Middeldorp, A. (ed.) RTA 2001. LNCS, vol. 2051, pp. 201–215. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  14. 14.
    Segoufin, L.: Typing and querying XML documents: some complexity bounds. In: Proc. PODS 2003, pp. 167–178. ACM Press, New York (2003)Google Scholar
  15. 15.
    Downey, R.G., Fellows, M.R.: Parametrized Complexity. Springer, Heidelberg (1999)CrossRefMATHGoogle Scholar
  16. 16.
    Gottlob, G., Koch, C., Pichler, R.: Efficient algorithms for processing XPath queries. In: Proc. VLDB 2002, pp. 95–106. Morgan Kaufmann, San Francisco (2002)Google Scholar
  17. 17.
    Gottlob, G., Koch, C., Pichler, R.: The complexity of XPath query evaluation. In: Proc. PODS 2003, pp. 179–190. ACM Press, New York (2003)Google Scholar
  18. 18.
    Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Reading (1994)MATHGoogle Scholar
  19. 19.
    Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)CrossRefMATHGoogle Scholar
  20. 20.
    Courcelle, B.: A representation of trees by languages I. Theoretical Computer Science 6, 255–279 (1978)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Anantharaman, S., Narendran, P., Rusinowitch, M.: Closure properties and decision problems of dag automata. Information Processing Letters 94, 231–240 (2005)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Markey, N., Schnoebelen, P.: A PTIME-complete matching problem for SLP-compressed words. Information Processing Letters 90, 3–6 (2004)MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Papadimitriou, C.H., Yannakakis, M.: On the complexity of database queries. Journal of Computer and System Sciences 58, 407–427 (1999)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Markus Lohrey
    • 1
  • Sebastian Maneth
    • 2
  1. 1.FMIUniversity of StuttgaertGermany
  2. 2.Faculté I & C, EPFLSwitzerland

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