Uncountable Automatic Classes and Learning

In this paper we consider uncountable classes recognizable by ω-automata and investigate suitable learning paradigms for them. In particular, the counterparts of explanatory, vacillatory and behaviourally correct learning are introduced for this setting. Here the learner reads in parallel the data of a text for a language L from the class plus an ω-index α and outputs a sequence of ω-automata such that all but finitely many of these ω-automata accept the index α iff α is an index for L. It is shown that any class is behaviourally correct learnable if and only if it satisfies Angluin’s tell-tale condition. For explanatory learning, such a result needs that a suitable indexing of the class is chosen. On the one hand, every class satisfying Angluin’s tell-tale condition is vacillatory learnable in every indexing; on the other hand, there is a fixed class such that the level of the class in the hierarchy of vacillatory learning depends on the indexing of the class chosen. We...

• Type: Conference
• Year: 2009
• Where: ALT
• Authors: Sanjay Jain, Qinglong Luo, Pavel Semukhin, Frank Stephan
• Keywords: ALT 2009, Angluin’s Tell-tale Condition, Correct Learning, Machine Learning, Suitable Learning Paradigms