SOS tasks are solvable under any number of crashes if and only if the graph of their output sets ordered by inclusion is connected (for t>0); all are solvable with no crashes.
The topological structure of asynchronous computability.J
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On the Decidability of Distributed Tasks with Output Sets under Asynchrony and Any Number of Crashes
SOS tasks are solvable under any number of crashes if and only if the graph of their output sets ordered by inclusion is connected (for t>0); all are solvable with no crashes.