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The Algebraic Theory of Context-Free Languages**This work was supported in part by the U.S. Army Signal Corps, the Air Force Office of Scientific Research, and the Office of Naval Research; and in part by the National Science Foundation; and in part by a grant from the Commonwealth Fund.

DOI: 10.1016/s0049-237x(09)70104-1
  • Linguistics


Publisher Summary This chapter describes 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. Language means simply a set of strings in some finite set V of symbols called the vocabulary of the language. Grammar essentially means a set of rules that give a recursive enumeration of the strings belonging to the language. It is noted that for a class of grammars to have linguistic interest, there must be a procedure that assigns to any pair (σ, G), where σ is a string and G a grammar of this class. In particular, the structural description indicates that the string σ is a well-formed sentence of the language L (G) generated by G. However, the chapter concerns with only one aspect of the structural description of a sentence—namely, its subdivision into phrases belonging to various categories.

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