# The topological structure of asynchronous computability

@article{Herlihy1999TheTS, title={The topological structure of asynchronous computability}, author={Maurice Herlihy and Nir Shavit}, journal={J. ACM}, year={1999}, volume={46}, pages={858-923} }

We give necessary and sufficient combinatorial conditions characterizing the tasks that can be solved by asynchronous processes, of which all but one can fail, that communicate by reading and writing a shared memory. We introduce a new formalism for tasks, based on notions from classical algebraic and combinatorial topology, in which a task''s possible input and output values are each associated with high-dimensional geometric structures called simplicial complexes. We characterize…

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