The Algebraic Theory of Context-Free Languages

Abstract

Publisher Summary This chapter discusses the several classes of sentence-generating devices that are closely related, in various ways, to the grammars of both natural languages and artificial languages of various kinds. By a language it simply mean a set of strings in some finite set V of symbols called the vocabulary of the language. By a grammar a set of rules that give a recursive enumeration of the strings belonging to the language. It can be said that the grammar generates these strings. The chapter discusses the aspect of the structural description of a sentence, namely, its subdivision into phrases belonging to various categories. A major concern of the general theory of natural languages is to define the class of possible strings; the class of possible grammars; the class of possible structural descriptions; a procedure for assigning structural descriptions to sentences, given a grammar; and to do all of this in such a way that the structural description assigned to a sentence by the grammar of a natural language will provide the basis for explaining how a speaker of this language would understand this sentence.