The topological structure of asynchronous computability

@article{Herlihy1999TheTS,
  title={The topological structure of asynchronous computability},
  author={M. Herlihy and N. 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… Expand
472 Citations

Paper Mentions

An algorithmic approach to the asynchronous computability theorem
  • 1
  • PDF
Towards a topological characterization of asynchronous complexity
  • 30
  • PDF
Toward a Topological Characterization of Asynchronous Complexity
  • 19
  • PDF
Geometric and combinatorial views on asynchronous computability
  • 3
  • Highly Influenced
  • PDF
From Geometric Semantics to Asynchronous Computability
  • 5
  • Highly Influenced
  • PDF
An Overview of Synchronous Message-Passing and Topology
  • 8
  • PDF
A Simple Algorithmic Characterization of Uniform Solvability (Extended Abstract)
  • Highly Influenced
Collapsibility of read/write models using discrete morse theory
  • 3
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 10 REFERENCES
Generalized FLP impossibility result for t-resilient asynchronous computations
  • 425
  • Highly Influential
Immediate atomic snapshots and fast renaming
  • 206
  • Highly Influential
Elements of algebraic topology
  • 2,399
  • Highly Influential
Distributed Computing: Fundamentals, Simulations and Advanced Topics
  • 1,051
  • Highly Influential
Algebraic Topology
  • 9,139
  • Highly Influential
  • PDF
Generalized p impossibility result for tresilient asynchronous computations
  • Proceedings of the 1993 ACM Symposium on Theory of Computing
  • 1993
The implications of the borowski-gafni simulation on the set consensus hierarchy
  • The implications of the borowski-gafni simulation on the set consensus hierarchy
  • 1993
GEOMETRICAL COMBINATORIAL TOPOLOGY VOL I
  • 32
  • Highly Influential
Geometrical Combinatorial Topology, v olume 1
  • Geometrical Combinatorial Topology, v olume 1
  • 1970
Geometrical combinatorial topology
  • 133
  • Highly Influential