Synthesizing Distributed Systems

In system synthesis, we transform a spe i ation into a system that is guaranteed to satisfy the spe i ation. When the system is distributed, the goal is to onstru t the system's underlying pro esses. Results on multi-player games imply that the synthesis problem for linear spe i ations is unde idable for general ar hite tures, and is nonelementary de idable for hierar hi al ar hite tures, where the pro esses are linearly ordered and information among them ows in one dire tion. In this paper we present a signi ant extension of this result. We handle both linear and bran hing spe i ations, and we show that a suÆ ient ondition for de idability of the synthesis problem is a linear or y li order among the pro esses, in whi h information ows in either one or both dire tions. We also allow the pro esses to have internal hidden variables, and we onsider ommuni ations with and without delay. Many pra ti al appli ations fall into this lass.