Formal languages: Origins and directions

1. IntIDduction My purpose is to survey the orlglns of the theory of formal languages and automata through 1964 and to indicate some of the main directions which the :-;ttldy of the sub4ect has takc::>n since tIlen. In the discussion of origins, I shall concentrate on those I know best: the work on mathematical linguistics and automatic translation of the 50s and early 60s, which led me into the field. I had hoped to trace the developments since 1964 thIDugh the papers presented at the IEEE Symposia on the FOill1dations of Computer Science (initia11v, Switching Circuit Theory and Logical Design; later, Switching and Automata TI1eory) and the companion, parvenu, AC11 Symposia on the Theory of Computing. This good intention was impossible to sustain, particularly as I moved fIDm the exuberant 60s into the grim 7 Os. LDng gone are the days in which abstracts of one's summer research and the theses of one's best students automatically appeared at the next Conference! Still I shall give pride of place to such cont1'ibutions where possible. There (:il'e at least five (not altogether distinct) sources foY' the ideas developed in fonnal language theory. They Eire: elogic and recursive function theory • s\vitching cil'cuit trleory c]IKl emodeling of biological systems., developm::ntal systems and eITBthematical and computational linguistics ·computer prograrmning and the of ALGOL and other Problem Qr)iented lrl.nguages Recursive function theory is ;:3urveyed elsewhel'C in these Proceedings so I shall mention relevant ideas only in passing. The emphasis of this paper is on formal languages, so I shall descrilR only the l'e-lated parts of the development of finite automata theory, skimping 01' skipping purely machine 01' system oriented topics. Phrase structure gpammars wen=? originally cle-scribed by Chomsky [l959a] as a forrna.lization of the Irrrrnediate Constituent (IC) analysis used by lin-tWists ~"'1 describing thp morpholog:/-aDd syntax' of natural languages. The work on :rn::lchine translation at various institutions used various theories as bases for automatic syntactic analysis t Th ·. and appropriate programming techniques were devised. At the same time, similar methods of syntax specification and programming techniques were used in the definition and implementation of Problem Oriented Programming Languages. In the early 60s, all of these various threads were brought together as it was recognized, and then formally proved, that all these models defined the same class of languages, namely, the family of context-free (CF) phrase structure languages. the publication of the tentative definition of …