# The asynchronous computability theorem for t-resilient tasks

@article{Herlihy1993TheAC, title={The asynchronous computability theorem for t-resilient tasks}, author={Maurice Herlihy and Nir Shavit}, journal={Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing}, year={1993} }

We give necessary and sufficient combinatorial conditions characterizing the computational tasks that can be solved by N asynchronous processes, up to t of which can fail by halting. The range of possible input and output values for an asynchronous task can be associated with a high-dimensional geometric structure called a simplicial complex. Our main theorem characterizes computability y in terms of the topological properties of this complex. Most notably, a given task is computable only if it…

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