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We consider an extension of the classical Total Store Order (TSO) semanticsby expanding it to turn-based 2-player safety games. During her turn, a playercan select any of the communicating processes and perform its next transition.We consider different formulations of the safety game problem depending onwhether one player or both of them transfer messages from the process buffersto the shared memory. We give the complete decidability picture for all thepossible alternatives.

TSO Games -- On the decidability of safety games under the total store order semantics (extended version with appendix)