The asynchronous computability theorem for t-resilient tasks

  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},
  • M. Herlihy, N. Shavit
  • Published 1 June 1993
  • Mathematics, Computer Science
  • Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing
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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