Locality, Reversibility, and Beyond: Learning Languages from Positive Data

Abstract

In algorithmic learning theory fundamental roles are played by the family of languages that are locally testable in the strict sense and by the family of reversible languages. These two families are shown to be the first two members of an infinite sequence of families of regular languages the members of which are learnable in the limit from positive data only. A uniform procedure is given for deciding, for each regular language R and each of our specified families, whether R belongs to the family. The approximation of arbitrary regular languages by languages belonging to these families is discussed. Further, we will give a uniform scheme for learning these families from positive data. Several research problems are also suggested.