Two schemes for the specification of translations on a context-free grammar are proposed. The first scheme, called a generalized syntax directed translation (GSDT), consists of a context free grammar with a set of semantic rules associated with each production of the grammar. In a GSDT an input word is parsed according to the underlying context free grammar, and at each node of the tree, a finite number of translation strings are computed in terms of the translation strings defined at the descendants of that node. The functional relationship between the length of input and length of output for translations defined by GSDT's is investigated. The second method for the specification of translations is in terms of tree automata-finite automata with output, walking on derivation trees of a context free grammar. It is shown that tree automata provide an exact characterization for those GSDT's with a linear relationship between input and output length. © 1972 Academic Press, Inc.
Aho, A. V., & Ullman, J. D. (1971). Translations on a context free grammar. Information and Control, 19(5), 439–475. https://doi.org/10.1016/S0019-9958(71)90706-6