An Axiomatic Approach to Computing the Connectivity of Synchronous and Asynchronous Systems

Authors:
Maurice Herlihy;Sergio Rajsbaum;Mark Tuttle
Affiliations:
Department of Computer Science, Brown University Providence, RI 02912, USA;Instituto de Matemáticas, UNAM, Ciudad Universitaria, D.F. 04510, Mexico;HP Labs, One Cambridge Center, Cambridge, MA 02142, USA
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2009

Citing 15
Cited 3

Agreement is harder than consensus: set consensus problems in totally asynchronous systems

PODC '90 Proceedings of the ninth annual ACM symposium on Principles of distributed computing
Generalized FLP impossibility result for t-resilient asynchronous computations

STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Set consensus using arbitrary objects (preliminary version)

PODC '94 Proceedings of the thirteenth annual ACM symposium on Principles of distributed computing
Impossibility of distributed consensus with one faulty process

Journal of the ACM (JACM)
Unifying synchronous and asynchronous message-passing models

PODC '98 Proceedings of the seventeenth annual ACM symposium on Principles of distributed computing
Round-by-round fault detectors (extended abstract): unifying synchrony and asynchrony

PODC '98 Proceedings of the seventeenth annual ACM symposium on Principles of distributed computing
Reaching Agreement in the Presence of Faults

Journal of the ACM (JACM)
The topological structure of asynchronous computability

Journal of the ACM (JACM)
Wait-Free k-Set Agreement is Impossible: The Topology of Public Knowledge

SIAM Journal on Computing
Tight bounds for k-set agreement

Journal of the ACM (JACM)
A Layered Analysis of Consensus

SIAM Journal on Computing
The Combinatorial Structure of Wait-free Solvable Tasks (Extended Abstract)

WDAG '96 Proceedings of the 10th International Workshop on Distributed Algorithms
tight bounds for k-set agreement with limited-scope failure detectors

Proceedings of the twenty-second annual symposium on Principles of distributed computing
Algebraic spans

Mathematical Structures in Computer Science
Distributed Computing: Fundamentals, Simulations and Advanced Topics

Distributed Computing: Fundamentals, Simulations and Advanced Topics

The topology of shared-memory adversaries

Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Concurrent computing and shellable complexes

DISC'10 Proceedings of the 24th international conference on Distributed computing
Simulations and reductions for colorless tasks

PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present a unified, axiomatic approach to proving lower bounds for the k-set agreement problem in both synchronous and asynchronous message-passing models. The proof involves constructing the set of reachable states, proving that these states are highly connected, and then appealing to a well-known topological result that high connectivity implies that set agreement is impossible. We construct the set of reachable states in an iterative fashion using a round operator that we define, and our proof of connectivity is an inductive proof based on this iterative construction and simple properties of the round operator.