LA- and PS-hierarchies in comparison

Abstract

Having presented two non-equivalent formalisms of generative grammar,¹ each with its own fully developed hierarchy of language and complexity classes, we return in this chapter to the formal properties of natural language. Section 12.1 compares the complexity of the LA- and PS-grammatical language classes. Section 12.2 describes the inclusion relations between language classes in the PS- and the LA-hierarchy, respectively. Section 12.3 defines a context-free language which is a C3-language. Section 12.4 describes the orthogonal relation between the context-free languages and the classes of C-languages. Section 12.5 investigates ambiguity in natural language, and concludes that the natural languages are in the class of C1-LAGs, thus parsing in linear time.