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LR Parsing for Global Index Languages (GILs)

  • José M. Castaño
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2759)

Abstract

We present here Global Index Grammars (GIGs) and the characterizing 2 Stack automaton model (LR-2PDA). We present the techniques to construct an LR parsing table for deterministic Global Index Grammars. GILs include languages which are beyond the power of Linear Indexed Grammars/Tree Adjoining Grammars. GILs generalize properties of CF Languages in a straightforward way and their descriptive power is relevant at least for natural language and molecular biology phenomena.

Keywords

Parsing Table Input Symbol Closure Operation Descriptive Power Formal Language Theory 
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.

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References

  1. [1]
    A.V. Aho. Indexed grammars — an extension of context-free grammars. Journal of the Association for Computing Machinery, 15(4):647–671, 1968.zbMATHMathSciNetGoogle Scholar
  2. [2]
    A.V. Aho, R. Sethi, and J.D. Ullman. Compilers: Principles, Techniques, and Tools. Addison-Wesley, Reading, MA, 1986.Google Scholar
  3. [3]
    M.A. Alonso, D. Cabrero, and M. Vilares. Construction of efficient generalized LR parsers. In Derick Wood and Sheng Yu, editors, Automata Implementation, volume 1436, pages 7–24. Springer-Verlag, Berlin-Heidelberg-New York, 1998.CrossRefGoogle Scholar
  4. [4]
    T. Becker. HyTAG: a new type of Tree Adjoining Grammars for Hybrid Syntactic Representation of Free Order Languages. PhD thesis, University of Saarbruecken, 1993.Google Scholar
  5. [5]
    R. Book. Confluent and other types of thue systems. J. Assoc. Comput. Mach., 29:171–182, 1982.zbMATHMathSciNetGoogle Scholar
  6. [6]
    J. Castaño. GIGs: Restricted context-sensitive descriptive power in bounded polynomial-time. In Proc. of Cicling 2003, Mexico City, February 16-22, 2003.Google Scholar
  7. [7]
    J. Castaño. Global index grammars, available at http://www.cs.brandeis.edu/~jcastano/GIGs.html. Ms., Computer Science Dept. Brandeis University, 2003.
  8. [8]
    J. Castaño. On the applicability of global index grammars. 2003. Student Workshop ACL.Google Scholar
  9. [9]
    A. Cherubini, L. Breveglieri, C. Citrini, and S. Reghizzi. Multipushdown languages and grammars. International Journal of Foundations of Computer Science, 7(3):253–292, 1996.zbMATHCrossRefGoogle Scholar
  10. [10]
    J. Dassow and G. Păun. Regulated Rewriting in Formal Language Theory. Springer, Berlin, Heidelberg, New York, 1989.Google Scholar
  11. [11]
    J. Dassow, G. Păun, and A. Salomaa. Grammars with controlled derivations. In G. Rozenberg and A. Salomaa, editors, Handbook of Formal Languages, Vol. 2. Springer, Berlin, 1997.Google Scholar
  12. [12]
    G. Gazdar. Applicability of indexed grammars to natural languages. In U. Reyle and C. Rohrer, editors, Natural Language Parsing and Linguistic Theories, pages 69–94. D. Reidel, Dordrecht, 1988.Google Scholar
  13. [13]
    T. Harju, O. Ibarra, J. Karhumäki, and A. Salomaa. Decision questions concerning semilinearity, morphisms and commutation of languages. In LNCS 2076, page 579ff. Springer, 2001.Google Scholar
  14. [14]
    M. H. Harrison. Introduction to Formal Language Theory. Addison-Wesley Publishing Company, Inc., Reading, MA, 1978.zbMATHGoogle Scholar
  15. [15]
    J. E. Hopcroft and Jeffrey D. Ullman. Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading, Massachusetts, 1979.zbMATHGoogle Scholar
  16. [16]
    N.A. Khabbaz. A geometric hierarchy of languages. Journal of Computer and System Sciences, 8(2):142–157, 1974.zbMATHMathSciNetCrossRefGoogle Scholar
  17. [17]
    D. Searls. Formal language theory and biological macromolecules. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, page 117ff, 1999.Google Scholar
  18. [18]
    H. Seki, T. Matsumura, M. Fujii, and T. Kasami. On multiple context-free grammars. Theoretical Computer. Science, pages 191–229, 1991.Google Scholar
  19. [19]
    K. Sikkel. Parsing schemata. Springer-Verlag, 1997.Google Scholar
  20. [20]
    M. Tomita. An efficiente augmented-context-free parsing algorithm. Computational linguistics, 13:31–46, 1987.Google Scholar
  21. [21]
    E. V. de la Clergerie and M.A. Pardo. A tabular interpretation of a class of 2-stack automata. In COLING-ACL, pages 1333–1339, 1998.Google Scholar
  22. [22]
    D.A. Walters. Deterministic context-sensitive languages: Part II. Information and Control, 17:41–61, 1970.zbMATHCrossRefMathSciNetGoogle Scholar
  23. [23]
    D. J. Weir. A geometric hierarchy beyond context-free languages. Theoretical Computer Science, 104(2):235–261, 1992.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • José M. Castaño
    • 1
  1. 1.Computer Science DepartmentBrandeis UniversityUSA

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