Abstract
A partial learner in the limit [16], given a representation of the target language (a text), outputs a sequence of conjectures, where one correct conjecture appears infinitely many times and other conjectures each appear a finite number of times. Following [5, 14], we define intrinsic complexity of partial learning, based on reducibilities between learning problems. Although the whole class of recursively enumerable languages is partially learnable (see [16]) and, thus, belongs to the complete learnability degree, we discovered a rich structure of incomplete degrees, reflecting different types of learning strategies (based, to some extent, on topological structures of the target language classes). We also exhibit examples of complete classes that illuminate the character of the strategies for partial learning of the hardest classes.
S. Jain—Supported in part by NUS grant numbers C252-000-087-001 and R146-000-181-112.
E. Kinber—Supported by URCG grant from Sacred Heart University.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Angluin, D.: Inductive inference of formal languages from positive data. Inf. Control 45, 117–135 (1980)
Angluin, D.: Learning regular sets from queries and counter-examples. Inf. Comput. 75, 87–106 (1987)
Blum, M.: A machine-independent theory of the complexity of recursive functions. J. ACM 14(2), 322–336 (1967)
Case, J., Kötzing, T.: Computability-theoretic learning complexity. Phil. Trans. R. Soc. London 370, 3570–3596 (2011)
Freivalds, R., Kinber, E., Smith, C.: On the intrinsic complexity of learning. Inf. Comput. 123(1), 64–71 (1995)
Gao, Z., Jain, S., Stephan, F.: On conservative learning of recursively enumerable languages. In: Bonizzoni, P., Brattka, V., Löwe, B. (eds.) CiE 2013. LNCS, vol. 7921, pp. 181–190. Springer, Heidelberg (2013)
Gao, Z., Jain, S., Stephan, F., Zilles, S.: A survey on recent results on partial learning. In: Proceedings of the Thirteenth Asian Logic Conference, pp. 68–92. World Scientific (2015)
Gold, E.M.: Language identification in the limit. Inf. Control 10(5), 447–474 (1967)
Gao, Z., Stephan, F.: Confident and consistent partial learning of recursive functions. In: Bshouty, N.H., Stoltz, G., Vayatis, N., Zeugmann, T. (eds.) ALT 2012. LNCS, vol. 7568, pp. 51–65. Springer, Heidelberg (2012)
Gao, Z., Stephan, F., Zilles, S.: Combining models of approximation with partial learning. In: Chaudhuri, K., Gentile, C., Zilles, S. (eds.) ALT 2015. LNSC (LNAI), vol. 9355, pp. 56–70. Springer, Heidelberg (2015)
Hopcroft, J., Ullman, J.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Boston (1979)
Jain, S., Kinber, E., Papazian, C., Smith, C., Wiehagen, R.: On the intrinsic complexity of learning recursive functions. Inf. Comput. 184(1), 45–70 (2003)
Jain, S., Kinber, E., Wiehagen, R.: Language learning from texts: degrees of intrinsic complexity and their characterizations. J. Comput. Syst. Sci. 63, 305–354 (2001)
Jain, S., Sharma, A.: The intrinsic complexity of language identification. J. Comput. Syst. Sci. 52, 393–402 (1996)
Jain, S., Stephan, F.: Consistent partial learning. In: Proceedings of the Twenty Second Annual Conference on Learning Theory (2009)
Osherson, D., Stob, M., Weinstein, S.: Systems that Learn: An Introduction to Learning Theory for Cognitive and Computer Scientists. MIT Press, Cambridge (1986)
Rogers, H.: Theory of Recursive Functions and Effective Computability. McGraw-Hill, New York (1967). Reprinted by MIT Press in 1987
Acknowledgements
We thank Frank Stephan and the referees for several helpful comments, which improved the presentation of the paper.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Jain, S., Kinber, E. (2016). Intrinsic Complexity of Partial Learning. In: Ortner, R., Simon, H., Zilles, S. (eds) Algorithmic Learning Theory. ALT 2016. Lecture Notes in Computer Science(), vol 9925. Springer, Cham. https://doi.org/10.1007/978-3-319-46379-7_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-46379-7_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-46378-0
Online ISBN: 978-3-319-46379-7
eBook Packages: Computer ScienceComputer Science (R0)