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The objective of this work is to expand the study of generalized finite automata theory by introducing generalized finite state mappings (finite state mappings of trees). In the process, we hope to provide an algebraic framework in which to study formalizations of transformations (in the sense that linguists use the term) and translations of natural and artificial languages. The concepts, “syntax directed translation” [2,18,19, 22, 29] and “transformation” [11, 25] can be formulated quite neatly within this framework. Sections 2 and 3 present basic concepts of generalized finite automata theory and its relationship to context-free languages. We provide some general notation for transformations in Section 4 and in the following four sections, two basic kinds of transformations will be introduced and certain fundamental properties proved. In Section 9, these definitions will be related to others in the literature and several areas for further investigation will be indicated.

Transformations and translations from the point of view of generalized finite automata theory