A Hierarchy of Language Families Learnable by Regular Language Learning

Abstract We shall establish the existence of a hierarchy of language families in which the learning problem for each family is reduced to the learning problem for regular languages. The hierarchy is defined inductively by controlling certain type of even linear grammars with languages in one family to yield languages in the next larger family. Each family contains the family of regular languages and has a nontrivial language such as {an1an2 ··· an2i| n ≥ 0}, where i is a nonnegative integer and each aj is a symbol. Thus this boosts the learnability of learning algorithms for regular languages.