Possibility and impossibility results in a shared memory environment

We focus on unreliable asynchronous shared memory model which support only atomic read and write operations. For such a model we provide a necessary condition for the solvability of problems in the presence of multiple undetectable crash failures. Also, by using game-theoretical notions, a necessary and sufficient condition is provided, for the solvability of problems in the presence of multiple undetectable initial failures (i.e., processes may fail only prior to the execution). Our results imply that many problems such as consensus, choosing a leader, ranking, matching and sorting are unsolvable in the presence of a single crash failure, and that variants of these problems are solvable in the presence of a single crash failure, and that variants of these problems are solvable in the presence of t - 1 crash failures but not in the presence of t crash failures. We show that a shared memory model can simulate various message passing models, and hence our impossibility results hold also for those message passing models. Our results extend and generalize previously known impossibility results for various asynchronous models.