Formal translations and the containment problem for Szilard languages

Abstract

One of the methods used for defining translations is the socalled syntax-directed translation scheme which can be interpreted as a pair of rather similar grammars with the productions working in parallel. Because of the similarity of the grammars each of the two grammars “fits” the other in the sense that for each derivation process in one grammar leading to a terminal word the corresponding derivation process in the other grammar also leads to a terminal word. For many practical applications it suffices to consider the case that one of the grammars fits the other, but not necessarily conversely. Investigating this idea, translations are obtained which are more powerful than the syntax-directed. It is shown that one can determine whether a given grammar fits another given grammar. As a by-product, it is established that the containment problem for Szilard languages is decidable.