Abstract
We introduce and explore a model for parallel learning of families of languages computable by finite automata. In this model, an algorithmic or automatic learner takes on n different input languages and identifies at least m of them correctly. For finite parallel learning, for large enough families, we establish a full characterization of learnability in terms of characteristic samples of languages. Based on this characterization, we show that it is the difference nāāām, the number of languages which are potentially not identified, which is crucial. Similar results are obtained also for parallel learning in the limit. We consider also parallel finite learnability by finite automata and obtain some partial results. A number of problems for automatic variant of parallel learning remain open.
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
Austinat, H., Diekert, V., Hertrampf, U., Petersen, H.: Regular frequency computations. Theoretical Computer ScienceĀ 330, 15ā20 (2005)
Angluin, D., Gasarch, W., Smith, C.: Training sequences. Theoretical Computer ScienceĀ 66, 255ā272 (1989)
Angluin, D.: Inductive inference of formal languages from positive data. Information and ControlĀ 45, 117ā135 (1980)
Blumensath, A., GrƤdel, E.: Automatic structures. In: 15th Annual IEEE Symposium on Logic in Computer Science (LICS), pp. 51ā62. IEEE Computer Society (2000)
Biegel, R., Gasarch, W., Kinber, E.: Frequency computation and bounded queries. Theoretical Computer ScienceĀ 163, 177ā192 (1996)
Balodis, K., Kucevalovs, I., Freivalds, R.: Frequency prediction of functions. In: KotĆ”sek, Z., Bouda, J., ÄernĆ”, I., Sekanina, L., Vojnar, T., AntoÅ”, D. (eds.) MEMICS 2011. LNCS, vol.Ā 7119, pp. 76ā83. Springer, Heidelberg (2012)
Gold, E.M.: Language identification in the limit. Information and ControlĀ 10(5), 447ā474 (1967)
Jain, S., Luo, Q., Stephan, F.: Learnability of automatic classes. Journal of Computer and System SciencesĀ 78(6), 1910ā1927 (2012)
Jain, S., Osherson, D., Royer, J., Sharma, A.: Systems that Learn: An Introduction to Learning Theory, 2nd edn. MIT Press, Cambridge (1999)
Kinber, E.: Frequency computations in finite automata. KibernetikaĀ 2, 7ā15 (1976) (in Russian); English translation in Cybernetics 12, 179ā187
Khoussainov, B., Nerode, A.: Automatic presentations of structures. In: Leivant, D. (ed.) LCC 1994. LNCS, vol.Ā 960, pp. 367ā392. Springer, Heidelberg (1995)
Kinber, E., Smith, C., Velauthapillai, M., Wiehagen, R.: On learning multiple concepts in parallel. Journal of Computer and System SciencesĀ 50, 41ā52 (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, pp. 127ā136. ACM Press (1993)
Mukouchi, Y.: Characterization of finite identification. In: Jantke, K.P. (ed.) AII 1992. LNCS, vol.Ā 642, pp. 260ā267. Springer, Heidelberg (1992)
Papadimitriou, C.H.S., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity. Dover (1998)
Pitt, L.: Probabilistic inductive inference. Journal of the ACMĀ 36, 383ā433 (1989)
Rose, G.: An extended notion of computability. Abstracts of International Congress for Logic, Methodology and Philosophy of Science, p. 14 (1960)
Smith, C.: The power of pluralism for automatic program synthesis. Journal of the ACMĀ 29, 1144ā1165 (1982)
Trakhtenbrot, B.: On the frequency of computation of functions. Algebra i LogikaĀ 2, 25ā32 (1964)
Wiehagen, R., Freivalds, R., Kinber, E.: On the power of probabilistic strategies in inductive inference. Theoretical Computer ScienceĀ 28, 111ā133 (1984)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
Ā© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Jain, S., Kinber, E. (2014). Parallel Learning of Automatic Classes of Languages. In: Auer, P., Clark, A., Zeugmann, T., Zilles, S. (eds) Algorithmic Learning Theory. ALT 2014. Lecture Notes in Computer Science(), vol 8776. Springer, Cham. https://doi.org/10.1007/978-3-319-11662-4_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-11662-4_6
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-11661-7
Online ISBN: 978-3-319-11662-4
eBook Packages: Computer ScienceComputer Science (R0)