Why extension-based proofs fail

@article{Alistarh2019WhyEP,
  title={Why extension-based proofs fail},
  author={Dan Alistarh and James Aspnes and Faith Ellen and Rati Gelashvili and Leqi Zhu},
  journal={Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing},
  year={2019}
}
  • Dan Alistarh, J. Aspnes, +2 authors Leqi Zhu
  • Published 4 November 2018
  • Computer Science
  • Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing
It is impossible to deterministically solve wait-free consensus in an asynchronous system. The classic proof uses a valency argument, which constructs an infinite execution by repeatedly extending a finite execution. We introduce extension-based proofs, a class of impossibility proofs that are modelled as an interaction between a prover and a protocol and that include valency arguments. Using proofs based on combinatorial topology, it has been shown that it is impossible to deterministically… 
8 Citations
Brief Announcement: Why Extension-Based Proofs Fail
TLDR
It is explained why it is impossible to deterministically solve k-set agreement among n > k ≥ 2 processes in a wait-free manner and, hence, extension-based proofs are limited in power.
Reductions and Extension-Based Proofs
TLDR
It is proved that, if T reduces to S, and T has an augmented extension-based proof that it is impossible to solve in the NIS model, then so does S.
Extension-Based Proofs for Synchronous Message Passing
TLDR
The result shows that no valency argument can prove the lower bound of t rounds for any k-set agreement algorithm among n > kt processes when at most k processes can crash each round.
Locally Solvable Tasks and the Limitations of Valency Arguments
TLDR
It is shown that a protocol can always solve such tasks locally, in the following sense: given a configuration and all its future valencies, if a single successor configuration is selected, then the protocol can reveal all decisions in this branch of executions, satisfying the task specification.
A Topological View of Partitioning Arguments: Reducing k-Set Agreement to Consensus
TLDR
This paper provides the topological representation of the reduction theorem, which reveals how partitioning is reflected in the protocol complex, and provides a way to construct a simple algorithm that solves set agreement.
A topological perspective on distributed network algorithms
TLDR
This work analyzes consensus, set-agreement, and approximate agreement in networks, and derives lower bounds for these problems under classical computational settings, such as the LOCAL model and dynamic networks.
A Topological Perspective on Distributed Network Algorithms
TLDR
This work analyzes consensus, set-agreement, and approximate agreement in networks, and derives lower bounds for these problems under classical computational settings, such as the LOCAL model and dynamic networks.
K-set agreement bounds in round-based models through combinatorial topology
TLDR
This work considers oblivious models, that is models where the set of possible graphs contains all graphs with more edges than some starting graphs, and derives lower bounds and upper bounds in one round for k-set agreement, such that these bounds are proved using combinatorial topology but stated only in terms of graph properties.

References

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Reductions and Extension-Based Proofs
TLDR
It is proved that, if T reduces to S, and T has an augmented extension-based proof that it is impossible to solve in the NIS model, then so does S.
Extension-Based Proofs for Synchronous Message Passing
TLDR
The result shows that no valency argument can prove the lower bound of t rounds for any k-set agreement algorithm among n > kt processes when at most k processes can crash each round.
Locally Solvable Tasks and the Limitations of Valency Arguments
TLDR
It is shown that a protocol can always solve such tasks locally, in the following sense: given a configuration and all its future valencies, if a single successor configuration is selected, then the protocol can reveal all decisions in this branch of executions, satisfying the task specification.
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TLDR
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TLDR
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TLDR
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TLDR
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TLDR
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TLDR
This paper generalizes FLP to multiple faults and establishes that k-set consensus proposed by Chaudhuri is impossible, if the protocol is to tolerate k failures, while there exists a protocol that tolerates k – 1 failures.
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