In the latter half of the 1950’s, Noam Chomsky began to develop mathematical models for the description of natural languages. Two disciplines originated in his work and have grown to maturity. The first of these is the theory of formal grammars, a branch of mathematics which has proven to be of great interest to information and computer sciences. The second is generative, or more specifically, transformational linguistics. Although these disciplines are independent and develop each according to its own aims and criteria, they remain closely interwoven. Without access to the theory of formal languages, for example, the contemporary study of the foundations of linguistics would be unthinkable.
The collaboration of Chomsky and the psycholinguist George Miller, around 1960, led to a considerable impact of transformational linguistics on the psychology of language. During a period of near feverish experimental activity, psycholinguists studied the various ways in which the new linguistic notions might be used in the development of models for language user and language acquisition. A good number of the original conceptions were naïve and could not withstand critical test, but in spite of this, generative linguistics has greatly influenced modern psycholinguistics.
The theory of formal languages, transformational linguistics, psycholinguistics, and their mutual relationships have been the theme of my three-volume book Formal Grammars in Linguistics and Psycholinguistics, published in 1974. Volume I of Formal Grammars was an introduction to the theory of formal languages and automata; grammars are treated only as formal systems in that volume. Volume II in turn dealt with applications of those mathematical models to linguistic theory. Volume III, finally, treated applications of grammatical systems to models of the language user and language learner, i.e., psycholinguistic applications. A new, single-volume edition of Formal Grammars is about to appear with John Benjamins Publishing Company.