Asynchronous games on Petri nets and ATL (2107.06866v1)

Abstract: We define a game on distributed Petri nets, where several players interact with each other, and with an environment. The players, or users, have perfect knowledge of the current state, and pursue a common goal. Such goal is expressed by Alternating-time Temporal Logic (ATL). The users have a winning strategy if they can cooperate to reach their goal, no matter how the environment behaves. We show that such a game can be translated into a game on concurrent game structures (introduced in order to give a semantics to ATL). We compare our game with the game on concurrent game structures and discuss the differences between the two approaches. Finally, we show that, when we consider memoryless strategies and a fragment of ATL, we can construct a concurrent game structure from the Petri net, such that an ATL formula is verified on the net if, and only if, it is verified on the game structure.