Morphic characterizations with insertion systems controlled by a context of length one
Among the variety of representation theorems for context-free languages, the Chomsky-Schutzenberger theorem is unique in that it consists of Dyck languages, regular languages, and simple operations. In the present paper, we obtain some characterizations of and representation theorems for languages in the Chomsky hierarchy by using insertion systems, strictly locally testable languages, and morphisms in the framework of the Chomsky-Schutzenberger theorem. For instance, each context-free language L can be represented in the form L = h(L(gamma) boolean AND R), where gamma is an insertion system of weight (1, 1), R is a strictly 2-testable language, and h is a morphism. In contrast, if R is instead a strictly 1-testable language, the class of languages generated is a proper subclass of context-free languages and incomparable with the class of regular languages. (c) 2012 Elsevier B.V. All rights reserved.
morphic characterization insertion system strictly locally testable language