New aspects of homomorphisms

Abstract

Homomorphisms have played an important role throughout the development of language theory. In the last years, new areas of language theory have been developed based on homomorphisms. We survey some recent results in such areas: Starting with the DOL equivalence problem we first mention the notions of homomorphism equivalence and equality sets, and their application to homomorphic representation theorems. We then use lengthpreserving homomorphisms to define grammatical similarity and discuss some striking results from the fast growing area of grammar forms and L forms.