Abstract
In this paper we explore the class of Strictly Piecewise languages, originally introduced to characterize long-distance phonotactic patterns by Heinz [7] as the Precedence Languages. We provide a series of equivalent abstract characterizations, discuss their basic properties, locate them relative to other well-known subregular classes and provide algorithms for translating between the grammars defined here and finite state automata as well as an algorithm for deciding whether a regular language is Strictly Piecewise.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Cancedda, N., Gaussier, E., Goutte, C., Renders, J.M.: Word-sequence kernels. Journal of Machine Learning Research 3, 1059–1082 (2003)
Chomsky, N.: Three models for the description of language. I.R.E. Transactions on Information Theory IT-2, 113–123 (1956); reprinted in Readings in Mathematical Psychology. In: Duncan Luce, R., Bush, R.R., Galanter, E. (eds.), vol. II, pp. 113–123. John Wiley & Sons, New York (1956)
Cook, E.D.: The synchronic and diachronic status of Sarcee gy. International Journal of American Linguistics 4, 192–196 (1978)
Cook, E.D.: A Sarcee Grammar. University of British Columbia Press (1984)
Grainger, J., Whitney, C.: Does the huamn mnid raed wrods as a wlohe? Trends in Cognitive Science 8, 58–59 (2004)
Hansson, G.: Theoretical and typological issues in consonant harmony. Ph.D. thesis, University of California, Berkeley (2001)
Heinz, J.: The Inductive Learning of Phonotactic Patterns. Ph.D. thesis, University of California, Los Angeles (2007)
Heinz, J.: Learning long distance phonotactics (2008) (submitted manuscipt)
Higman, G.: Ordering by divisibility in abstract algebras. Proceedings of the London Mathmatical Society 2, 326–336 (1952)
Hopcroft, J., Motwani, R., Ullman, J.: Introduction to Automata Theory. In: Languages, and Computation. Addison-Wesley, Reading (2001)
Joshi, A.K.: Tree-adjoining grammars: How much context sensitivity is required to provide reasonable structural descriptions? In: Dowty, D., Karttunen, L., Zwicky, A. (eds.) Natural Language Parsing, pp. 206–250. Cambridge University Press, Cambridge (1985)
Kobele, G.: Generating Copies: An Investigation into Structural Identity in Language and Grammar. Ph.D. thesis, University of California, Los Angeles (2006)
Kontorovich, L.A., Cortes, C., Mohri, M.: Kernel methods for learning languages. Theoretical Computer Science 405(3), 223–236 (2008)
Lodhi, H., Cristianini, N., Shawe-Taylor, J., Watkins, C.: Text classification using string kernels. Journal of Machine Language Research 2, 419–444 (2002)
Lothaire, M. (ed.): Combinatorics on Words. Cambridge University Press, Cambridge (1997)
McNaughton, R., Papert, S.: Counter-Free Automata. MIT Press, Cambridge (1971)
Rogers, J., Pullum, G.: Aural pattern recognition experiments and the subregular hierarchy. In: Kracht, M. (ed.) Proceedings of 10th Mathematics of Language Conference, pp. 1–7. University of California, Los Angeles (2007)
Rose, S., Walker, R.: A typology of consonant agreement as correspondence. Language 80(3), 475–531 (2004)
Sakarovitch, J., Simon, I.: Subwords. In: Lothaire, M. (ed.) Combinatorics on Words, Encyclopedia of Mathematics and Its Applications, vol. 17, ch. 6, pp. 105–134. Addison-Wesley, Reading (1983)
Shawe-Taylor, J., Christianini, N.: Kernel Methods for Pattern Analysis. Cambridge University Press, Cambridge (2005)
Shieber, S.: Evidence against the context-freeness of natural language. Linguistics and Philosophy 8, 333–343 (1985)
Simon, I.: Piecewise testable events. In: Brakhage, H. (ed.) GI-Fachtagung 1975. LNCS, vol. 33, pp. 214–222. Springer, Heidelberg (1975)
Trahtman, A.: Piecewise and local threshold testability of DFA. In: Freivalds, R. (ed.) FCT 2001. LNCS, vol. 2138, pp. 347–358. Springer, Heidelberg (2001)
Whitney, C., Cornelissen, P.: SERIOL reading. Language and Cognitive Processes 23, 143–164 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Rogers, J. et al. (2010). On Languages Piecewise Testable in the Strict Sense. In: Ebert, C., Jäger, G., Michaelis, J. (eds) The Mathematics of Language. MOL MOL 2009 2007. Lecture Notes in Computer Science(), vol 6149. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14322-9_19
Download citation
DOI: https://doi.org/10.1007/978-3-642-14322-9_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14321-2
Online ISBN: 978-3-642-14322-9
eBook Packages: Computer ScienceComputer Science (R0)