A LTL Fragment for GR(1)-Synthesis

The idea of automatic synthesis of reactive programs starting from temporal logic (LTL) specifica-tions is quite old, but was commonly thought to be infeasible due to the known double exponentialcomplexity of the problem. However, new ideas have recently renewed the interest in LTL synthesis:One major new contribution in this area is the recent work of Piterman et al. who showed how poly-nomial time synthesis can be achieved for a large class of LTL specifications that is expressive enoughto cover many practical examples. These LTL specifications are equivalent to w-automata having aso-called GR(1) acceptance condition. This approach has been used to automatically synthesize im-plementations of real-world applications. To this end, manually written deterministic w-automatahaving GR(1) conditions were used instead of the original LTL specifications. However, manuallygenerating deterministic monitors is, of course, a hard and error-prone task. In this paper, we there-fore present algorithms to automatically translate specifications of a remarkable large fragment ofLTL to deterministic monitors having a GR(1) acceptance condition so that the synthesis algorithmscan start with more readable LTL specifications.