Solving parallel equations over $\omega$-regular languages

We consider the problem of deriving a component of a system that combined with a known part of a system meets the given specification. We assume that the behavior of the overall system and of its parts is described by Buchi automata that accept $\omega$-regular languages, i.e. languages containing infinite words. The problem of deriving an unknown component can be casted into the problem of solving language equations over $\omega$-regular languages. However solving techniques for equations over regular languages cannot be directly applied to the case of $\omega$-regular languages.