Learning Languages in the Limit from Positive Information with Finitely Many Memory Changes

TL;DR

This paper explores the capabilities of bounded memory inductive learners in language identification, establishing a comprehensive hierarchy of success criteria and their interrelations, with implications for iterative learning models.

Contribution

It provides a complete classification of success criteria for bounded memory learners and shows equivalences and differences between iterative and bounded memory learning under various restrictions.

Findings

Non-U-shapedness is not restrictive for bounded memory learning.

Conservativeness and strong monotonicity are compatible with bounded memory learning.

Iterative and bounded memory learning are equivalent under many semantic restrictions.

Abstract

We investigate learning collections of languages from texts by an inductive inference machine with access to the current datum and a bounded memory in form of states. Such a bounded memory states (BMS) learner is considered successful in case it eventually settles on a correct hypothesis while exploiting only finitely many different states. We give the complete map of all pairwise relations for an established collection of criteria of successfull learning. Most prominently, we show that non-U-shapedness is not restrictive, while conservativeness and (strong) monotonicity are. Some results carry over from iterative learning by a general lemma showing that, for a wealth of restrictions (the semantic restrictions), iterative and bounded memory states learning are equivalent. We also give an example of a non-semantic restriction (strongly non-U-shapedness) where the two settings differ.