Abstract
Automatic classes are classes of languages for which a finite automaton can decide whether a given element is in a set given by its index. The present work studies the learnability of automatic families by automatic learners which, in each round, output a hypothesis and update a long term memory, depending on the input datum, via an automatic function, that is, via a function whose graph is recognised by a finite automaton. Many variants of automatic learners are investigated: where the long term memory is restricted to be the just prior hypothesis whenever this exists, cannot be of size larger than the size of the longest example or has to consist of a constant number of examples seen so far. Furthermore, learnability is also studied with respect to queries which reveal information about past data or past computation history; the number of queries per round is bounded by a constant. These models are generalisations of the model of feedback queries, given by Lange, Wiehagen and Zeugmann.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Angluin, D.: Inductive inference of formal languages from positive data. Information and Control 45, 117–135 (1980)
Angluin, D.: Finding patterns common to a set of strings. Journal of Computer and System Sciences 21, 46–62 (1980)
Angluin, D.: Inference of reversible languages. Journal of the ACM 29, 741–765 (1982)
Angluin, D.: Learning regular sets from queries and counterexamples. Information and Computation 75, 87–106 (1987)
Blum, L., Blum, M.: Toward a mathematical theory of inductive inference. Information and Control 28, 125–155 (1975)
Blumensath, A., Grädel, E.: Automatic structures. In: 15th Annual IEEE Symposium on Logic in Computer Science (LICS), pp. 51–62. IEEE Computer Society, Los Alamitos (2000)
Case, J., Jain, S., Lange, S., Zeugmann, T.: Incremental concept learning for bounded data mining. Information and Computation 152, 74–110 (1999)
Case, J., Jain, S., Le, T.D., Ong, Y.S., Semukhin, P., Stephan, F.: Automatic learning of subclasses of pattern languages. In: Dediu, A.-H. (ed.) LATA 2011. LNCS, vol. 6638, pp. 192–203. Springer, Heidelberg (2011)
Fernau, H.: Identification of function distinguishable languages. Theoretical Computer Science 290, 1679–1711 (2003)
Freivalds, R., Kinber, E., Smith, C.H.: On the impact of forgetting on learning machines. Journal of the Association of Computing Machinery 42, 1146–1168 (1995)
Mark Gold, E.: Language identification in the limit. Information and Control 10, 447–474 (1967)
Hodgson, B.R.: Théories décidables par automate fini. Ph.D. thesis, University of Montréal (1976)
Hodgson, B.R.: Décidabilité par automate fini. Annales des sciences mathématiques du Québec 7(1), 39–57 (1983)
Jain, S., Luo, Q., Stephan, F.: Learnability of automatic classes. In: Dediu, A.-H., Fernau, H., Martín-Vide, C. (eds.) LATA 2010. LNCS, vol. 6031, pp. 321–332. Springer, Heidelberg (2010)
Jain, S., Ong, Y.S., Pu, S., Stephan, F.: On automatic families. TRB1/10, School of Computing, National University of Singapore (2010)
Khoussainov, B., Nerode, A.: Automatic presentations of structures. In: Leivant, D. (ed.) LCC 1994. LNCS, vol. 960, pp. 367–392. Springer, Heidelberg (1995)
Kinber, E., Stephan, F.: Language learning from texts: mind changes, limited memory and monotonicity. Information and Computation 123, 224–241 (1995)
Lange, S., Zeugmann, T.: Language learning in dependence on the space of hypotheses. In: Proceedings of the Sixth Annual Conference on Computational Learning Theory (COLT), pp. 127–136. ACM Press, New York (1993)
Lange, S., Zeugmann, T.: Incremental learning from positive data. Journal of Computer and System Sciences 53, 88–103 (1996)
Lange, S., Zeugmann, T., Zilles, S.: Learning indexed families of recursive languages from positive data: a survey. Theoretical Computer Science 397, 194–232 (2008)
Osherson, D., Stob, M., Weinstein, S.: Systems That Learn, An Introduction to Learning Theory for Cognitive and Computer Scientists. The MIT Press, Cambridge (1986)
Rubin, S.: Automatic Structures. Ph.D. Thesis, The University of Auckland (2004)
Rubin, S.: Automata presenting structures: a survey of the finite string case. The Bulletin of Symbolic Logic 14, 169–209 (2008)
Wexler, K., Culicover, P.W.: Formal Principles of Language Acquisition. The MIT Press, Cambridge (1980)
Wiehagen, R.: Limes-Erkennung rekursiver Funktionen durch spezielle Strategien. Elektronische Informationsverarbeitung und Kybernetik (EIK) 12, 93–99 (1976)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Case, J., Jain, S., Ong, Y.S., Semukhin, P., Stephan, F. (2011). Automatic Learners with Feedback Queries. In: Löwe, B., Normann, D., Soskov, I., Soskova, A. (eds) Models of Computation in Context. CiE 2011. Lecture Notes in Computer Science, vol 6735. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21875-0_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-21875-0_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21874-3
Online ISBN: 978-3-642-21875-0
eBook Packages: Computer ScienceComputer Science (R0)