Distributed Games with Causal Memory Are Decidable for Series-Parallel Systems

This paper deals with distributed control problems by means of distributed games played on Mazurkiewicz traces. The main difference with other notions of distributed games recently introduced is that, instead of having a local view, strategies and controllers are able to use a more accurate memory, based on their causal view. Our main result states that using the causal view makes the control synthesis problem decidable for series-parallel systems for all recognizable winning conditions on finite behaviors, while this problem with local view was proved undecidable even for reachability conditions.