  We consider the models of distributed computation defined as subsets of the
runs of the iterated immediate snapshot model. Given a task $T$ and a model
$M$, we provide topological conditions for $T$ to be solvable in $M$. When
applied to the wait-free model, our conditions result in the celebrated
Asynchronous Computability Theorem (ACT) of Herlihy and Shavit. To demonstrate
the utility of our characterization, we consider a task that has been shown
earlier to admit only a very complex $t$-resilient solution. In contrast, our
generalized computability theorem confirms its $t$-resilient solvability in a
straightforward manner.
