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Petri games are a multi-player game model for the automatic synthesis ofdistributed systems, where the players are represented as tokens on a Petri netand are grouped into environment players and system players. As long as theplayers move in independent parts of the net, they do not know of each other;when they synchronize at a joint transition, each player gets informed of theentire causal history of the other players.  We show that the synthesis problem for two-player Petri games under a globalsafety condition is NP-complete and it can be solved within a non-deterministicexponential upper bound in the case of up to 4 players. Furthermore, we showthe undecidability of the synthesis problem for Petri games with at least 6players under a local safety condition.

(Un)Decidability Bounds of the Synthesis Problem for Petri Games