Abstract
Linear indexed grammars (LIGs) can be used to describe nonlocal dependencies. The indexing mechanism, however, can only account for dependencies that are nested. In natural languages one can easily find examples to which this simple model cannot be applied straight forwardly. In this paper I will show that a formalism fitting better to linguistic structures can be obtained by using a sequence of pushdowns instead of one pushdown for the storage of the indices in a derivation. Crucially, we have to avoid unwanted interactions between the push-downs that would make possible the simulation of a turing machine. [1] solves this problem for multi– pushdown automata by restricting reading to the first nonempty pushdown. I will argue that the corresponding restriction on writing is more natural from a linguistic point of view. I will show that, under each of both restrictions, grammars with a sequence of n pushdowns give rise to a subclass of the nth member of the hierarchy defined by [15,16], and therefore are mildly context sensitive.
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References
Breveglieri, L., A. Cherubini, C. Citrini, and S. Crespi Reghizzi. Multi–push–down languages and grammars. International Journal of Foundations of Computer Science, 7(3): 253–291, 1996.
Chomsky, N. The Minimalist Program. MIT Press, Cambridge, MA, 1995.
Ferguson, K. S., and E. M. Groat. Defining “shortest move”, deriving A–movement, strict cyclicity and incorporation phenomena. In GLOW Newsletter 32, 1994.
Gazdar, G. 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.
Lewis, R. L. Interference in short–term memory: The magical number two (or three) in sentence processing. Journal of Psycholinguistic Research, 25(1):93–115, 1996.
Michaelis, J., and C. Wartena. How linguistic constraints on movement conspire to yield languages analyzable with a restricted form of LIGs. In Proceedings of the Conference on Formal Grammar (FG’ 97), pages 158–168, Aix en Provence, 1997.
Michaelis, J., and C. Wartena. LIGs with reduced derivation sets. In Bouma, G., G.-J. M. Kruijff, E. Hinrichs, and R. T. Oehrle, editors, Constraints and Resources in Natural Language Syntax and Semantics, volume II of Studies in Constrained Based Lexicalism, pages 263–279. CSLI Publications, Stanford, CA, 1999.
Rado, J. Topic–focus vs. background: The role of structural information in discourse interpretation. PhD thesis, University of Massachusetts, Amherst, MA, 1997.
Rambow, O. Formal and Computational Aspects of Natural Language Syntax. PhD thesis, University of Pennsylvania, 1994.
Rizzi, L. Relativized Minimality. MIT Press, Cambridge, MA, 1990.
Rogers, J. On descriptive complexity, language complexity, and GB. In Black-burn, P., and M. de Rijke, editors, Specifying Syntactic Structures, chapter 6. Cambridge University Press, 1997.
Rudin, C. On multiple question and multiple wh–fronting. Natural Language and Linguistic Theory, 6:445–501, 1988.
Stabler, E. P. The finite connectivity of linguistic structure. In Clifton, C., L. Frazier, and K. Rayner, editors, Perspectives on Sentence Processing, chapter 13, pages 303–336. Lawrence Erlbaum, Hillsdale, NJ, 1994.
Vogler, H. Iterated linear control and iterated one–turn pushdowns. Mathematical Systems Theory, 19(2):117–133, 1986.
Weir, D. J. Characterizing Mildly Context–Sensitive Grammar Formalisms. PhD thesis, University of Pennsylvania, 1988.
Weir, D. J. A geometric hierarchy beyond context–free languages. Theoretical Computer Science, 104(4):235–261, 1992.
Weir, D. J. Linear iterated pushdowns. Computational Intelligence, 10(4):422–430, 1994.
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Wartena, C. (1999). Grammars with Composite Storages. In: Moortgat, M. (eds) Logical Aspects of Computational Linguistics. LACL 1998. Lecture Notes in Computer Science(), vol 2014. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45738-0_16
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DOI: https://doi.org/10.1007/3-540-45738-0_16
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