Abstract

Among the variety of representation theorems for context-free languages, the Chomsky–Schützenberger 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–Schützenberger theorem. For instance, each context-free language L can be represented in the form L=h(L(γ)∩R), where γ 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.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.