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Pumping, Shrinking and Pronouns: From Context Free to Indexed Grammars

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7810))

Abstract

Pumping-shrinking operation is a useful tool in the study of Formal Languages. A pump-shrink bound for Linear Indexed Grammars is derived, depending only on the the number of auxiliary symbols of the grammar. Observations are suggested on formal operations analogous to shrinking of subordinate clauses.

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References

  1. Aho, A.V.: Indexed grammars. J. Assoc. Comput. Mach. 15, 647–671 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bar-Hillel, Y., Perles, M., Shamir, E.: On formal properties of simple Phrase Structure Grammars. Z. Phonetik Sprachwiss. Kommunikat. 14, 143–172 (1961)

    MathSciNet  MATH  Google Scholar 

  3. Gazdar, G.: Applicability of Indexed Grammars to Natural Languages. In: Reyle, U., Rohrer, C. (eds.) Natural Language Parsing and Linguistic Theories, pp. 69–94 (1988)

    Google Scholar 

  4. Gilman, R.: A Shrinking Lemma for Indexed Languages. Theo. Comp. Sci. 16, 277–281 (1996)

    Article  MathSciNet  Google Scholar 

  5. Hayashi, T.: On Derivation Trees of Indexed Grammars: An extension of the wvwxy-Theorem. Publ. RIMS Kyoto Univ. 9, 61–92 (1973)

    Article  MATH  Google Scholar 

  6. Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading (1979)

    MATH  Google Scholar 

  7. Keller, B., Weir, D.: A Tractable Extension of Linear Indexed Grammars. In: Proc. EACL, pp. 75–82 (1995)

    Google Scholar 

  8. Maier, W., Sogaard, A.: Treebanks and Mild Context - Sensitivity. In: Proc. of Conference on Formal Grammar (FG 2008), pp. 16–76 (2008)

    Google Scholar 

  9. Ogden, W.: Intercalation theorems for Stack Languages. In: Proc. First Annual ACM Symposium of the Theory of Computing, pp. 31–42 (1969)

    Google Scholar 

  10. Saginer, Y.: Fast unsupervised Incremental Parsing. In: Proc. ACL, vol. 45, pp. 384–389 (2007)

    Google Scholar 

  11. Shamir, E.: Some Inherently ambiguous Context-Free Languages. Inf. and Control 18, 355–363 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  12. Staudacher, P.: New frontiers beyond Context-Freeness: DI-grammars and DI-automata. In: Proc. 6th EACL (1993)

    Google Scholar 

  13. Vijay-Shanker, K.: A study of Tree Adjoining Grammars. Ph.D. Thesis, U. Penn (1988)

    Google Scholar 

  14. Vijay-Shanker, K., Weir, D.J.: Parsing some constrained grammar-formalisms. Computational Linguistics 19, 591–636 (1993)

    Google Scholar 

  15. Vijay-Shanker, K., Weir, D.J.: The equivalence of four extensions of Context-Free Grammars. Math. Sys. Theory 27, 511–546 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  16. Vijay-Shanker, K., Weir, D.J., Joshi, A.K.: Characterizing structural descriptions produced by various grammatical formalisms. In: Proc. 25th ACL, pp. 104–111 (1987)

    Google Scholar 

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Shamir, E. (2013). Pumping, Shrinking and Pronouns: From Context Free to Indexed Grammars. In: Dediu, AH., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2013. Lecture Notes in Computer Science, vol 7810. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37064-9_45

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  • DOI: https://doi.org/10.1007/978-3-642-37064-9_45

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-37063-2

  • Online ISBN: 978-3-642-37064-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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