String Extension Learning Using Lattices
The class of regular languages is not identifiable from positive data in Gold’s language learning model. Many attempts have been made to define interesting classes that are learnable in this model, preferably with the associated learner having certain advantageous properties. Heinz ’09 presents a set of language classes called String Extension (Learning) Classes, and shows it to have several desirable properties.
In the present paper, we extend the notion of String Extension Classes by basing it on lattices and formally establish further useful properties resulting from this extension. Using lattices enables us to cover a larger range of language classes including the pattern languages, as well as to give various ways of characterizing String Extension Classes and its learners. We believe this paper to show that String Extension Classes are learnable in a very natural way, and thus worthy of further study.
KeywordsMinimum Element Computable Function Inductive Inference Regular Language Language Class
Unable to display preview. Download preview PDF.
- 3.Bārzdiņš, J.: Inductive inference of automata, functions and programs. In: Proceedings of the 20th International Congress of Mathematicians, Vancouver, Canada, pp. 455–560 (1974); English translation in American Mathematical Society Translations 2, 109, 107–112 (1977)Google Scholar
- 4.Birkhoff, G.: Lattice Theory. American Mathematical Society, Providence (1984)Google Scholar
- 9.Fernau, H.: Identification of function distinguishable languages. Theoretical Computer Science 290(3) (2003)Google Scholar
- 10.Fulk, M.: A Study of Inductive Inference Machines. PhD thesis, SUNY at Buffalo (1985)Google Scholar
- 12.Heinz, J.: String extension learning (2009), http://phonology.cogsci.udel.edu/~heinz/papers/heinz-sel.pdf
- 13.Jain, S., Osherson, D., Royer, J., Sharma, A.: Systems that Learn: An Introduction to Learning Theory, 2nd edn. MIT Press, Cambridge (1999)Google Scholar
- 14.Jantke, K.P.: Monotonic and non-monotonic inductive inference. New Generation Computing 8(4) (1991)Google Scholar
- 16.Nation, J.: Notes on lattice theory (2009), http://www.math.hawaii.edu/~jb/books.html
- 17.Osherson, D., Stob, M., Weinstein, S.: Systems that Learn: An Introduction to Learning Theory for Cognitive and Computer Scientists. MIT Press, Cambridge (1986)Google Scholar
- 19.Royer, J., Case, J.: Subrecursive Programming Systems: Complexity and Succinctness. In: Research monograph in Progress in Theoretical Computer Science. Birkhäuser, Boston (1994)Google Scholar
- 20.Weinstein, S.: Private communication at the Workshop on Learnability Theory and Linguistics. University of Western Ontario (1982)Google Scholar
- 21.Wexler, K., Culicover, P.: Formal Principles of Language Acquisition. MIT Press, Cambridge (1980)Google Scholar