Model-based software development processes often force their users to translate instances of one modeling language into related instances of another modeling language and vice-versa. The underlying data structure of such languages usually are some sort of graphs. Triple graph grammars (TGGs) are a formally founded language for describing correspondence relationships between two graph languages in a declarative way. Bidirectional graph language translators can be derived from a TGG, which maps pairs of related graph instances onto each other. These translators must fulfill certain compatibility properties with respect to the correspondence relationships established by their TGG. These properties are guaranteed for the original TGG approach as published 15 years ago. However, its expressiveness is pushed to the limit in most real world scenarios. Furthermore, the original approach relies on a parsing algorithm with exponential runtime complexity. In this contribution, we study a more expressive class of TGGs with
negative application conditions
and show for the first time that derived translators with a polynomial runtime complexity still preserve the above mentioned compatibility properties. For this purpose, we introduce a new characterization of well-formed TGGs together with a new translation rule scheduling algorithm that considers
of input graphs.