ACM Transactions on Programming Languages and Systems (TOPLAS)
Generalized FLP impossibility result for t-resilient asynchronous computations
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Wait-free k-set agreement is impossible: the topology of public knowledge
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
The asynchronous computability theorem for t-resilient tasks
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
More choices allow more faults: set consensus problems in totally asynchronous systems
Information and Computation
Sharing memory robustly in message-passing systems
Journal of the ACM (JACM)
Failure detectors and the wait-free hierarchy (extended abstract)
Proceedings of the fourteenth annual ACM symposium on Principles of distributed computing
Unreliable failure detectors for reliable distributed systems
Journal of the ACM (JACM)
The weakest failure detector for solving consensus
Journal of the ACM (JACM)
k-set agreement with limited accuracy failure detectors
Proceedings of the nineteenth annual ACM symposium on Principles of distributed computing
Distributed computing: fundamentals, simulations and advanced topics
Distributed computing: fundamentals, simulations and advanced topics
The weakest failure detectors to solve certain fundamental problems in distributed computing
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
The combined power of conditions and failure detectors to solve asynchronous set agreement
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Irreducibility and additivity of set agreement-oriented failure detector classes
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
On the weakest failure detector ever
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Test & Set, Adaptive Renaming and Set Agreement: a Guided Visit to Asynchronous Computability
SRDS '07 Proceedings of the 26th IEEE International Symposium on Reliable Distributed Systems
(Almost) all objects are universal in message passing systems
DISC'05 Proceedings of the 19th international conference on Distributed Computing
Weakening failure detectors for k-set agreement via the partition approach
DISC'07 Proceedings of the 21st international conference on Distributed Computing
Local Maps: New Insights into Mobile Agent Algorithms
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
(anti-Ωx × Σz)-based k-set agreement algorithms
OPODIS'10 Proceedings of the 14th international conference on Principles of distributed systems
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One of the most celebrated results of the theory of distributed computing is the impossibility, in an asynchronous system of n processes that communicate through shared memory registers, to solve the set agreement problem where the processes need to decide on up to n-1 among their n initial values. In short, the result indicates that the register abstraction is too weak to implement the set agreement one. This paper explores the relation between these abstractions in a message passing system where a register is not a given physical device but is rather itself implemented by processes communicating through message passing. We show that, maybe surprisingly, the information about process failures that is necessary and sufficient to implement a register shared by two particular processes is sufficient but not necessary to implement set agreement. We later generalize this result by considering k-set agreement, where the processes can decide on up to k values, and comparing it with a register shared by any particular subset of 2k processes. We prove that, for 1 ≤ k ≤ n/2, (a) any failure information that is sufficient to implement a register shared by 2k processes is sufficient to implement (n-k)-set agreement but (b) a failure information that is sufficient for (n-k)-set agreement is not sufficient for a register shared by 2k processes. We also prove that (c) a failure information that is sufficient for a register shared by 2k processes is not sufficient for ((n-k)-1)-set agreement.