# 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} }

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…

## Figures and Topics from this paper

## 8 Citations

Brief Announcement: Why Extension-Based Proofs Fail

- Computer SciencePODC
- 2020

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

- Computer SciencePODC
- 2021

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

- Computer ScienceDISC
- 2021

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

- Computer ScienceOPODIS
- 2020

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

- Computer ScienceSSS
- 2019

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

- Computer ScienceTheor. Comput. Sci.
- 2021

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

- Computer ScienceSIROCCO
- 2019

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

- Computer SciencePODC
- 2020

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.

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