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Reachability in Distributed Memory Automata

11 We introduce Distributed Memory Automata, a model of register automata suitable to capture 12 some features of distributed algorithms designed for shared memory systems. In this model, each 13 participant owns a local register and a shared register and has the ability to change its local value, 14 to write it in the global memory and to test atomically the number of occurrences of its value in 15 the shared memory, up to some threshold. We show that the control state reachability problem for 16 Distributed Memory Automata is Pspace -complete for a ﬁxed number of participants and is in 17 Pspace when the number of participants is not ﬁxed a priori. 18