Formal Translations and Szilard Languages

One of the m e thods for def ining t ranslat ions is the so called syntax-di rec ted t rans la t ion scheme which can be in terpre ted as a pair of ra ther s imilar g rammars wi th the product ions work ing in parallel. Because of the s imilar i ty of the g r a m m a r s each of the two g rammars "f i ts" the other in the sense tha t for each der ivat ion process in one g r a m m a r leading to a te rminal word the cor responding der ivat ion process in the other g r a m m a r also leads to a te rminal word. For many pract ical applicat ions it suffices to consider the case that one of the g rammars fits the other, bu t not necessari ly conversely. Inves t iga t ing this idea, t ranslat ions are obta ined which are more powerful than the syntax-directed. I t is shown tha t one can de te rmine whe the r a given g r a m m a r fits another given grammar . As a by-product , it is es tabl ished tha t the con ta inment p rob lem for Szitard languages is decidable.