Learning Languages by Collecting Cases andTuning

We investigate the problem of case-based learning of formal languages. Case-based reasoning and learning is a currently booming area of artiicial intelligence. The formal framework for case-based learning of languages has recently been developed by JL93] in an inductive inference manner. In this paper, we rst show that any indexed class of recursive languages in which niteness is decidable is case-based representable, but many classes of languages including the class of all regular languages are not case-based learnable with a xed universal similarity measure, even if both positive and negative examples are presented. Next we consider a framework of case-based learning where the learning algorithm is allowed to learn similarity measures, too. To avoid trivial encoding tricks, we carefully examine to what extent the similarity measure is going to be learned. Then by allowing only to learn a few parameters in the similarity measures, we show that any indexed class of recursive languages whose niteness problem is decidable is case-based learnable. This implies that all context-free languages are case-based learnable by collecting cases and learning parameters of the similarity measures.