Are two contex-free languages translatable in a syntax-directed translation scheme?

Syntax Directed Translation Schemes (SDTS's) are a formalism for describing the process of translation within a syntax directed compiler. In this scheme each production of the source context-free grammarG1 is coupled with a production of the object context-free grammarG2.In this paper the problem of characterizing the possibility of translating the source language into an object language by means of a SDTS is studied. Such a scheme is obtained by modifyingG1 andG2 in order to construct two grammarsG1' andG2' which can be coupled in a SDTS.G1' andG2' have productions corresponding to derivatives inG1 andG2. It is shown that for fixed maximum length of such derivatives it is effectively decidable whether a SDTS exists which translatesL (G1) intoL (G2).