Prescribed Learning of Indexed Families

Article type: Research Article

Authors: Jain, Sanjay | Stephan, Frank | Nan, Ye

Affiliations: School of Computing, National University of Singapore, Singapore 117590, Republic of Singapore. E-mails: sanjay@comp.nus.edu.sg; g0701171@nus.edu.sg | Department of Mathematics, National University of Singapore, Singapore 117543, Republic of Singapore. E-mail: fstephan@comp.nus.edu.sg

Abstract: This work extends studies of Angluin, Lange and Zeugmann on how learnability of a language class depends on the hypothesis space used by the learner. While previous studies mainly focused on the case where the learner chooses a particular hypothesis space, the goal of this work is to investigate the case where the learner has to cope with all possible hypothesis spaces. In that sense, the present work combines the approach of Angluin, Lange and Zeugmann with the question of how a learner can be synthesized. The investigation for the case of uniformly r.e. classes has been done by Jain, Stephan and Ye [6]. This paper investigates the case for indexed families and gives a special attention to the notions of conservative and non U-shaped learning.

Keywords: Inductive inference, prescribed learning, uniform learning, indexed families, conservative learning

Journal: Fundamenta Informaticae, vol. 83, no. 1-2, pp. 159-175, 2008