Many aspects of formal languages

Abstract

Formal language theory is, together with automata theory, which is really inseparable from language theory, the oldest branch of theoretical computer science. Indeed, the role of language theory in computer science is analogous to that of philosophy in general science: it constitutes the stem from which the more specialized branches of knowledge emerge. A typical example is seen from the early history of complexity theory. That formal language theory is really an interdisciplinary area of science is seen, for instance, from the fact that different branches of language theory are closely connected with pure algebra, linguistics of natural languages, programming languages, compilers, computer graphics, and the description of the development of simple organisms. The strength of formal language theory has been in its ability to create new models for new investigation, rather than sticking to a specific fixed model. There is no reason to doubt this ability in the future. The purpose of this paper is to give some glimpses of the diverse investigations referred to in the preceding paragraph. Section 1 is concerned with fundamental issues; more details are contained in Salomaa (1973) [3] and Salomaa (1985) [5]. A problem going back to the beginning of this century is discussed in Section 2; the reader may consult also Salomaa (1981) [4] and Thue [8]. The final section discusses a very recent problem in cryptography; Salomaa (to be published) [6] is a general book about cryptography and data security.