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
Aho, A.V.: Indexed grammars. J. Assoc. Comput. Mach. 15, 647–671 (1968)
Bar-Hillel, Y., Perles, M., Shamir, E.: On formal properties of simple Phrase Structure Grammars. Z. Phonetik Sprachwiss. Kommunikat. 14, 143–172 (1961)
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)
Gilman, R.: A Shrinking Lemma for Indexed Languages. Theo. Comp. Sci. 16, 277–281 (1996)
Hayashi, T.: On Derivation Trees of Indexed Grammars: An extension of the wvwxy-Theorem. Publ. RIMS Kyoto Univ. 9, 61–92 (1973)
Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading (1979)
Keller, B., Weir, D.: A Tractable Extension of Linear Indexed Grammars. In: Proc. EACL, pp. 75–82 (1995)
Maier, W., Sogaard, A.: Treebanks and Mild Context - Sensitivity. In: Proc. of Conference on Formal Grammar (FG 2008), pp. 16–76 (2008)
Ogden, W.: Intercalation theorems for Stack Languages. In: Proc. First Annual ACM Symposium of the Theory of Computing, pp. 31–42 (1969)
Saginer, Y.: Fast unsupervised Incremental Parsing. In: Proc. ACL, vol. 45, pp. 384–389 (2007)
Shamir, E.: Some Inherently ambiguous Context-Free Languages. Inf. and Control 18, 355–363 (1971)
Staudacher, P.: New frontiers beyond Context-Freeness: DI-grammars and DI-automata. In: Proc. 6th EACL (1993)
Vijay-Shanker, K.: A study of Tree Adjoining Grammars. Ph.D. Thesis, U. Penn (1988)
Vijay-Shanker, K., Weir, D.J.: Parsing some constrained grammar-formalisms. Computational Linguistics 19, 591–636 (1993)
Vijay-Shanker, K., Weir, D.J.: The equivalence of four extensions of Context-Free Grammars. Math. Sys. Theory 27, 511–546 (1994)
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)
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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
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