Abstract
We introduce an algorithm that learns the class of Tier-based Strictly k-Local (TSL\(_k\)) formal languages in polynomial time on a sample of positive data whose size is bounded by a constant. The TSL\(_k\) languages are useful in modeling the cognition of sound patterns in natural language [6, 11], and it is known that they can be efficiently learned from positive data in the case that \(k=2\) [9]. We extend this result to any k and improve on its time efficiency. We also refine the definition of a canonical TSL\(_k\) grammar and prove several properties about these grammars that aid in their learning.
We thank Jane Chandlee, Gunnar Hansson, Jeff Heinz, and three reviewers.
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References
GarcÃa, P., Vidal, E., Oncina, J.: Learning locally testable languages in the strict sense. In: Proceedings of Workshop on Algorithmic Learning Theory, pp. 325–338 (1990)
Gold, M.E.: Language identification in the limit. Inf. Control 10, 447–474 (1967)
Heinz, J.: The inductive learning of phonotactic patterns. Ph.D. thesis, University of California, Los Angeles (2007)
Heinz, J.: Learning long-distance phonotactics. Linguist. Inq. 41, 623–661 (2010)
Heinz, J.: Computational phonology part I: foundations. Lang. Linguist. Compass 5(4), 140–152 (2011)
Heinz, J., Rawal, C., Tanner, H.G.: Tier-based strictly local constraints for phonology. In: Proceedings of 49th Annual Meeting of the Association for Computational Linguistics, pp. 58–64. Association for Computational Linguistics, Portland, June 2011
de la Higuera, C.: Characteristic sets for polynomial grammatical inference. Mach. Learn. 27(2), 125–138 (1997)
Jardine, A.: Learning tiers for long-distance phonotactics. In: Proceedings of 6th Conference on Generative Approaches to Language Acquisition North America (GALANA 2015), pp. 60–72 (2016)
Jardine, A., Heinz, J.: Learning tier-based strictly 2-local languages. Trans. Assoc. Comput. Linguist. 4, 87–98 (2016)
Jurafsky, D., Martin, J.H.: Speech and Language Processing, 2nd edn. Pearson Prentice Hall, Upper Saddle River (2009)
McMullin, K.: Tier-based locality in long-distance phonotactics: learnability and typology. Ph.D. thesis, University of British Columbia (2016)
McMullin, K., Hansson, G.Ó: Long-distance phonotactics as tier-based strictly 2-local languages. In: Proceedings of 2014 Annual Meeting on Phonology. Linguistic Society of America, Washington, DC (2016)
McNaughton, R., Papert, S.: Counter-Free Automata. MIT Press, Cambridge (1971)
Nevins, A.: Locality in Vowel Harmony. No. 55 in Linguistic Inquiry Monographs. MIT Press, Cambridge (2010)
Odden, D.: Adjacency parameters in phonology. Language 70(2), 289–330 (1994)
Rogers, J., Heinz, J., Fero, M., Hurst, J., Lambert, D., Wibel, S.: Cognitive and sub-regular complexity. In: Morrill, G., Nederhof, M.-J. (eds.) FG 2012-2013. LNCS, vol. 8036, pp. 90–108. Springer, Heidelberg (2013). doi:10.1007/978-3-642-39998-5_6
Rogers, J., Pullum, G.: Aural pattern recognition experiments and the subregular hierarchy. J. Log. Lang. Inf. 20, 329–342 (2011)
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Jardine, A., McMullin, K. (2017). Efficient Learning of Tier-Based Strictly k-Local Languages. In: Drewes, F., MartÃn-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2017. Lecture Notes in Computer Science(), vol 10168. Springer, Cham. https://doi.org/10.1007/978-3-319-53733-7_4
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