Abstract
We present a measure of cognitive complexity for subclasses of the regular languages that is based on model-theoretic complexity rather than on description length of particular classes of grammars or automata. Unlike description length approaches, this complexity measure is independent of the implementation details of the cognitive mechanism. Hence, it provides a basis for making inferences about cognitive mechanisms that are valid regardless of how those mechanisms are actually realized.
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Folia, V., Uddén, J., de Vries, M., Forkstam, C., Petersson, K.M.: Artificial language learning in adults and children. Language Learning 60, 188–220 (2010)
Hauser, M.D., Chomsky, N., Fitch, W.T.: The faculty of language: What is it, who has it, and how did it evolve? Science 298(5598), 1569–1579 (2002)
Heinz, J.: Learning long-distance phonotactics. Linguistic Inquiry 41(4), 623–661 (2010)
Heinz, J., Idsardi, W.: Sentence and word complexity. Science 333(6040), 295–297 (2011)
McNaughton, R., Papert, S.: Counter-Free Automata. MIT Press (1971)
Büchi, J.R.: Weak second-order arithmetic and finite automata. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 6, 66–92 (1960)
Elgot, C.C.: Decision problems of finite automata and related arithmetics. Transactions of the American Mathematical Society 98, 21–51 (1961)
Hayes, B.: Metrical Stress Theory. Chicago University Press (1995)
van der Hulst, H., Goedemans, R., van Zanten, E. (eds.): A survey of word accentual patterns in the languages of the world. Mouton de Gruyter, Berlin (2010)
Heinz, J.: The Inductive Learning of Phonotactic Patterns. PhD thesis, University of California, Los Angeles (2007)
Heinz, J.: On the role of locality in learning stress patterns. Phonology 26(2), 303–351 (2009)
Hopcroft, J., Motwani, R., Ullman, J.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley (2001)
Kracht, M.: The Mathematics of Language. Mouton de Gruyter (2003)
Enderton, H.B.: A Mathematical Introduction to Logic. Academic Press (1972)
Gold, E.: Language identification in the limit. Information and Control 10, 447–474 (1967)
Garcia, P., Vidal, E., Oncina, J.: Learning locally testable languages in the strict sense. In: Proceedings of the Workshop on Algorithmic Learning Theory, pp. 325–338 (1990)
Edlefsen, M., Leeman, D., Myers, N., Smith, N., Visscher, M., Wellcome, D.: Deciding strictly local (SL) languages. In: Breitenbucher, J. (ed.) Proceedings of the Midstates Conference for Undergraduate Research in Computer Science and Mathematics, pp. 66–73 (2008)
Heinz, J.: UD phonology lab stress pattern database (March 2012), http://phonology.cogsci.udel.edu/dbs/stress/
Graf, T.: Comparing incomparable frameworks: A model theoretic approach to phonology. University of Pennsylvania Working Papers in Linguistics 16(2), Article 10 (2010), http://repository.upenn.edu/pwpl/vol16/iss1/10
Hyman, L.M.: How (not) to do phonological typology: the case of pitch-accent. Language Sciences 31(2-3), 213–238 (2009); Data and Theory: Papers in Phonology in Celebration of Charles W. Kisseberth
García, P., Ruiz, J.: Learning k-testable and k-piecewise testable languages from positive data. Grammars 7, 125–140 (2004)
Thomas, W.: Classifying regular events in symbolic logic. Journal of Computer and Systems Sciences 25, 360–376 (1982)
Rogers, J., Heinz, J., Bailey, G., Edlefsen, M., Visscher, M., Wellcome, D., Wibel, S.: On languages piecewise testable in the strict sense. In: Ebert, C., Jäger, G., Michaelis, J. (eds.) MOL 10. LNCS (LNAI), vol. 6149, pp. 255–265. Springer, Heidelberg (2010)
Simon, I.: Piecewise testable events. In: Brakhage, H. (ed.) GI-Fachtagung 1975. LNCS, vol. 33, pp. 214–222. Springer, Heidelberg (1975)
Graf, T.: Locality and the complexity of minimalist derivation tree languages. In: de Groote, P., Nederhof, M.-J. (eds.) Formal Grammar 2010/2011. LNCS, vol. 7395, pp. 208–227. Springer, Heidelberg (2012)
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Rogers, J., Heinz, J., Fero, M., Hurst, J., Lambert, D., Wibel, S. (2013). Cognitive and Sub-regular Complexity. In: Morrill, G., Nederhof, MJ. (eds) Formal Grammar. FG FG 2013 2012. Lecture Notes in Computer Science, vol 8036. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39998-5_6
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DOI: https://doi.org/10.1007/978-3-642-39998-5_6
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