Skip to main content
SpringerLink
Log in

Languages Modulo Normalization

  • Conference paper
Frontiers of Combining Systems (FroCoS 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4720))

Included in the following conference series:

Abstract

We propose a new class of tree automata, called tree automata with normalization (TAN). This framework is obtained by extending equational tree automata, and improves the results of the previous work, such as: recognized tree languages modulo the idempotency f(x,x) = x are closed under complement, which are not closed in equational tree automata, besides we do not lose important decidability. In the paper, first we investigate the closure properties of this class for Boolean operations and the decidability relative to the equational tree automata. Next we consider the relationship to other automata frameworks, in particular, hedge automata, which is a class of unranked tree automata. Hedge automata have been recognized in the XML database community as a theoretical basis for modeling the manipulation of semi-structured data. Through the observation about transformations from hedge automata to tree automata, we discuss advantages in the expressiveness and complexity of TAN. As an application of our framework, we show an example that XML schema with constraints that can not be dealt with by other tree automata frameworks is manipulated by TAN.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

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

    Google Scholar 

  2. Carme, J., Niehren, J., Tommasi, M.: Querying Unranked Trees with Stepwise Tree Automata. In: van Oostrom, V. (ed.) RTA 2004. LNCS, vol. 3091, pp. 235–236. Springer, Heidelberg (2004)

    Google Scholar 

  3. Comon, H., Dauchet, M., Gilleron, R., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree Automata Techniques and Applications, draft (2005), available at http://www.grappa.univ-lille3.fr/tata

  4. Comon, H., Jacquemard, F.: Ground Reducibility is EXPTIME-Complete, Information and Computation, vol. 187(1), pp. 123–153. Elsevier, Amsterdam (2003)

    Google Scholar 

  5. Contejean, E., Marché, C., Monate, B., Urbain, X.: The CiME System: Version 2.02, Software and the document (2004), available at http://cime.lri.fr/

  6. Dal Zilio, S., Lugiez, D.: XML Schema, Tree Logic and Sheaves Automata. In: Applicable Algebra in Engineering, Communication and Computing, vol. 17(5), pp. 337–377. Springer, Heidelberg (2006)

    Google Scholar 

  7. Engelfriet, J., Maneth, S.: A Comparison of Pebble Tree Transducers with Macro Tree Transducers. In: Acta Informatica, vol. 39, pp. 613–698. Springer, Heidelberg (2003)

    Google Scholar 

  8. Feuillade, G., Genet, T., Viet Triem Tong, V.: Reachability Analysis over Term Rewriting Systems. Journal of Automated Reasoning 33, 341–383 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  9. Hendrix, J., Meseguer, J., Ohsaki, H.: A Sufficient Completeness Checker for Linear Order-Sorted Specifications Modulo Axioms. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 151–155. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  10. Hendrix, J., Ohsaki, H., Viswanathan, M.: Propositional Tree Automata. In: Pfenning, F. (ed.) RTA 2006. LNCS, vol. 4098, pp. 50–65. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  11. Hosoya, H., Vouillon, J., Pierce, B.C.: Regular Expression Types for XML. In: Proc. of 5th ICFP, Montreal (Canada), vol. 35(9), pp. 11–22. ACM, New York (2000)

    Chapter  Google Scholar 

  12. Klarlund, N., Møller, A.: MONA Version 1.4 User Manual, BRICS Notes Series NS-01-1, Department of Computer Science, University of Aarhus (2001)

    Google Scholar 

  13. Kutsia, T.: Solving Equations Involving Sequence Variables and Sequence Functions. In: Buchberger, B., Campbell, J.A. (eds.) AISC 2004. LNCS (LNAI), vol. 3249, pp. 157–170. Springer, Heidelberg (2004)

    Google Scholar 

  14. Lugiez, D.: Multitree Automata That Count. In: Theoretical Computer Science, vol. 333(1–2), pp. 225–263. Elsevier, Amsterdam (2005)

    Google Scholar 

  15. Maneth, S., Perst, T., Seidl, H.: XML Type Checking in Polynomial Time. In: Schwentick, T., Suciu, D. (eds.) ICDT 2007. LNCS, vol. 4353, pp. 254–268. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  16. Marché, C.: Normalized Rewriting: An Alternative to Rewriting Modulo a Set of Equations. Journal of Symbolic Computation 21(3), 253–288 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  17. Milo, T., Suciu, D., Vianu, V.: Typechecking for XML Transformers. In: Proc. of 19th PODS, Dallas (Texas), pp. 11–22. ACM, New York (2000)

    Google Scholar 

  18. Murata, M.: Hedge Automata: A Formal Model for XML Schemata, draft (2000), available at http://citeseer.ist.psu.edu/murata99hedge.html

  19. Murata, M., Prescod, P.: SGML/XML and Forest/Hedge Automata Theory, Online Resource for Markup Language Technologies, Cover Pages, OASIS (May 2001), Online document available at http://xml.coverpages.org/hedgeAutomata.html

  20. Ohsaki, H., Seki, H.: Languages Modulo Normalization, draft (2007) Available at http://staff.aist.go.jp/hitoshi.ohsaki/

  21. Ohsaki, H., Takai, T.: ACTAS: A System Design for Associative and Commutative Tree Automata Theory. In: Proc. of 5th RULE, Aachen (Germany), vol. ENTCS124, pp. 97–111. Elsevier, Amsterdam (2005)

    Google Scholar 

  22. Ohsaki, H., Takai, T.: Decidability and Closure Properties of Equational Tree Languages. In: Tison, S. (ed.) RTA 2002. LNCS, vol. 2378, pp. 114–128. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  23. Ohsaki, H.: Beyond Regularity: Equational Tree Automata for Associative and Commutative Theories. In: Fribourg, L. (ed.) CSL 2001 and EACSL 2001. LNCS, vol. 2142, pp. 539–553. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  24. Parikh, R.: On Context-Free Languages. JACM 13(4), 570–581 (1966)

    Article  MATH  MathSciNet  Google Scholar 

  25. Seidl, H., Schwentick, T., Muscholl, A.: Numerical Document Queries. In: Proc. of 22nd PODS, San Diego (California), pp. 155–166. ACM Press, New York (2003)

    Google Scholar 

  26. Takai, T., Kaji, Y., Seki, H.: Right-Linear Finite Path Overlapping Term Rewriting Systems Effectively Preserve Recognizability. In: Bachmair, L. (ed.) RTA 2000. LNCS, vol. 1833, pp. 246–260. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  27. Thatcher, J.W.: Characterizing Derivation Trees of Context-Free Grammars Through a Generalization of Automata Theory. Journal of Computer and System Sciences 1(4), 317–322 (1967)

    MATH  MathSciNet  Google Scholar 

  28. Verma, K.N.: Two-Way Equational Tree Automata for AC-Like Theories: Decidability and Closure Properties. In: Nieuwenhuis, R. (ed.) RTA 2003. LNCS, vol. 2706, pp. 180–197. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  29. Verma, K.N.: On Closure under Complementation of Equational Tree Automata for Theories Extending AC. In: Vardi, M.Y., Voronkov, A. (eds.) LPAR 2003. LNCS, vol. 2850, pp. 183–197. Springer, Heidelberg (2003)

    Google Scholar 

  30. Extensible Markup Language (XML) Schema 1.0, 3rd edn., W3C (2004) Document available at http://www.w3.org/TR/2004/REC-xml-20040204/

Download references

Author information

Authors and Affiliations

  1. National Institute of Advanced Industrial Science and Technology,  

    Hitoshi Ohsaki

  2. Nara Institute of Science and Technology,  

    Hiroyuki Seki

Authors
  1. Hitoshi Ohsaki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hiroyuki Seki
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Boris Konev Frank Wolter

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ohsaki, H., Seki, H. (2007). Languages Modulo Normalization . In: Konev, B., Wolter, F. (eds) Frontiers of Combining Systems. FroCoS 2007. Lecture Notes in Computer Science(), vol 4720. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74621-8_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-74621-8_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74620-1

  • Online ISBN: 978-3-540-74621-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation