  We present a novel method for the synthesis of finite state systems that is a
generalisation of the generalised reactivity(1) synthesis approach by Piterman,
Pnueli and Sa'ar. In particular, we describe an efficient method to synthesize
systems from linear-time temporal logic specifications for which all
assumptions and guarantees have a Rabin index of one. We show how to build a
parity game with at most five colours that captures all solutions to the
synthesis problem from such a specification. This parity game has a structure
that is amenable to symbolic implementations. We furthermore show that the
results obtained are in some sense tight, i.e., that there does not exist a
similar synthesis method for assumptions and specifications of higher Rabin
index, unless P=NP.
