# Language learning with a bounded number of mind changes

## Abstract

We study the learnability of enumerable families \(\mathcal{L}\) of uniformly recursive languages in dependence on the number of allowed mind changes, i.e., with respect to a well-studied measure of efficiency. We distinguish between *exact* learnability (\(\mathcal{L}\) has to be inferred w.r.t. \(\mathcal{L}\)) and *class preserving* learning (\(\mathcal{L}\) has to be inferred w.r.t. some suitable chosen enumeration of all the languages from \(\mathcal{L}\)) as well as between learning from *positive* and from both, *positive and negative* data.

The measure of efficiency is applied to prove the superiority of class preserving learning algorithms over exact learning. We considerably improve results obtained previously and establish two infinite hierarchies. Furthermore, we separate exact and class preserving learning from positive data that avoids *overgeneralization*. Finally, language learning with a bounded number of mind changes is completely characterized in terms of recursively generable finite sets. These characterizations offer a new method to handle overgeneralizations and resolve an open question of Mukouchi (1992).

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