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Tree Automata and XPath on Compressed Trees

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Book cover Implementation and Application of Automata (CIAA 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3845))

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Abstract

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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References

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  4. Bryant, R.E.: Symbolic boolean manipulation with ordered binary-decision diagrams. ACM Computing Surveys 24, 293–318 (1992)

    Article  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. Maneth, S., Busatto, G.: Tree transducers and tree compressions. In: Walukiewicz, I. (ed.) FOSSACS 2004. LNCS, vol. 2987, pp. 363–377. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  8. Comon, H., Dauchet, M., Gilleron, R., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree automata techniques and applications (2002), available on: http://www.grappa.univ-lille3.fr/tata

  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)

    Chapter  Google Scholar 

  10. Gécseg, F., Steinby, M.: Tree automata. Akadémiai Kiadó (1984)

    Google Scholar 

  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. Neven, F.: Automata theory for XML researchers. SIGMOD Record 31, 39–46 (2002)

    Article  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. Downey, R.G., Fellows, M.R.: Parametrized Complexity. Springer, Heidelberg (1999)

    Book  MATH  Google Scholar 

  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. 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. Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Reading (1994)

    MATH  Google Scholar 

  19. Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)

    Book  MATH  Google Scholar 

  20. Courcelle, B.: A representation of trees by languages I. Theoretical Computer Science 6, 255–279 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  21. Anantharaman, S., Narendran, P., Rusinowitch, M.: Closure properties and decision problems of dag automata. Information Processing Letters 94, 231–240 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  22. Markey, N., Schnoebelen, P.: A PTIME-complete matching problem for SLP-compressed words. Information Processing Letters 90, 3–6 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  23. Papadimitriou, C.H., Yannakakis, M.: On the complexity of database queries. Journal of Computer and System Sciences 58, 407–427 (1999)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. FMI, University of Stuttgaert, Germany

    Markus Lohrey

  2. Faculté I & C, EPFL, Switzerland

    Sebastian Maneth

Authors
  1. Markus Lohrey
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  2. Sebastian Maneth
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Editor information

Editors and Affiliations

  1. Sophia Antipolis, Laboratoire I3S, Les Algorithmes - bât. Euclide B, Université de Nice, 2000, route des lucioles, BP 121, 06903, Sophia Antipolis - Cedex, France

    Jacques Farré

  2. Sophia Antipolis, Ecole Polytechnique, Université de Nice, 930, route des colles, BP 145, 06903, Sophia Antipolis - Cedex, France

    Igor Litovsky

  3. Laboratoire I3S, Université de Nice, Sophia Antipolis & CNRS, France

    Sylvain Schmitz

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© 2006 Springer-Verlag Berlin Heidelberg

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Lohrey, M., Maneth, S. (2006). Tree Automata and XPath on Compressed Trees. In: Farré, J., Litovsky, I., Schmitz, S. (eds) Implementation and Application of Automata. CIAA 2005. Lecture Notes in Computer Science, vol 3845. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11605157_19

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  • DOI: https://doi.org/10.1007/11605157_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31023-5

  • Online ISBN: 978-3-540-33097-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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