Abstract
We review the properties of Global Index Grammars (GIGs), a grammar formalism that uses a stack of indices associated with productions and has restricted context-sensitive power. We show how the control of the derivation is performed and how this impacts in the descriptive power of this formalism both in the string languages and the structural descriptions that GIGs can generate.
Similar content being viewed by others
References
Aho, A.V., 1968, “Indexed grammars – An extension of context-free grammars,” Journal of the Association for Computing Machinery 15, 647–671.
Boullier, P., 2003, “Counting with range concatenation grammars,” Theoretical Computer Science 293, 391–416.
Castañ,o, J., 2003a, “GIGs: Restricted context-sensitive descriptive power in bounded polynomial time,” in Proceedings of Cicling 2003, Mexico City, February 16–22.
Castaño, J., 2003b, “LR Parsing for Global Index Languages (GILs),” in Proceeding of CIAA 2003; Santa Barbara, CA.
Castaño, J., 2004, “Global index languages,” Ph.D. Thesis, Brandeis University, Department of Computer Science, Waltham, MA.
Cherubini, A., Breveglieri, L., Citrini, C., and Reghizzi, S., 1996, “Multipushdown languages and grammars,” International Journal of Foundations of Computer Science 7, 253–292.
Dassow, J. and Păun, G., 1989, Regulated Rewriting in Formal Language Theory, Berlin, Heidelberg, New York: Springer.
Dassow, J., Pàun, G., and Salomaa, A., 1997, “Grammars with controlled derivations,” in Handbook of Formal Language, Vol. 2, G. Rozenberg and A. Salomaa, eds., Berlin: Springer.
Gazdar, G., 1988, “Applicability of indexed grammars to natural languages,” pp. 69–94 in Natural Language Parsing and Lingustic Theories, U. Reyle and C. Rohrer, eds., Dordrecht: D. Reidel.
Harju, T., Ibarra, O., Karhumäki, J., and Salomaa, A., 2001, “Decision questions concerning semilinearity, morphisms and commutation of languages,” pp. 579–590 in LNCS 2076.Springer.
Harrison, M.H., 1978, Introduction to Formal Language Theory, Reading, MA: Addison-Wesley Publishing Commany, Inc.
Joshi, A., 1985, “Tree adjoining grammars: How much context-sensitivity is required to provide reasonable structural description?,” pp. 206–250 in Natural Language Processing: Psycholinguistic, Computational and Theoretical Perspectives, D. Dowty, L. Karttunen, and A. Zwicky, eds., New York: Chicago University Press.
Joshi, A. 2000, “Relationship between strong and weak generative power of formal systems,” pp. 107–114 in Proceedings of the Fifth International Workshop on Tree Adjoining Grammars and Related Formalisms (TAG+5). Paris, France.
Joshi, A., Vijay-Shanker, K., and Weir, D., 1991, “The convergence of mildly context sensitive grammatical formalisms,” pp. 31–81 in Foundational Issues in Natural Language Processing, P. Sells, S. Shieber, and T. Wasow, eds., Cambridge, MA: MIT Press.
Khabbaz, N.A., 1974, “A geometric hierarchy of languages,” Journal of Computer and System Sciences 8, 142–157.
Miller, P., 1999, Strong Generative Capacity, Stanford, CA: CSLI Publications, Stanford University.
Seki, H., Matsumura, T., Fujii, M., and Kasami, T., 1991, “On multiple context free grammars,” Theoretical Computer Science, 191–229.
Steedman, M., 1985, “Dependency and coordination in the grammar of Dutch and English,” Language, 523–568.
Vijay-Shanker, K., Weir, D.J., and Joshi, A.K., 1987, “Characterizing structural descriptions produced by various grammatical formalisms,” pp. 104–111 in Proceeding of the 25th ACL. Stanford, CA.
Weir, D., 1988, “Characterizing mildly context-sensitive grammar formalisms,” Ph.D. Thesis, University of Pennsylvania.
Weir, D., 1992, “A geometric hierarchy beyond context-free languages,” Theoretical Computer Science 104, 235–261.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Castaño, J.M. Global Index Grammars and Descriptive Power. J Logic Lang Inf 13, 403–419 (2004). https://doi.org/10.1007/s10849-004-2113-y
Issue Date:
DOI: https://doi.org/10.1007/s10849-004-2113-y