Atomic snapshots of shared memory
PODC '90 Proceedings of the ninth annual ACM symposium on Principles of distributed computing
ACM Transactions on Programming Languages and Systems (TOPLAS)
Immediate atomic snapshots and fast renaming
PODC '93 Proceedings of the twelfth 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
More choices allow more faults: set consensus problems in totally asynchronous systems
Information and Computation
Impossibility of distributed consensus with one faulty process
Journal of the ACM (JACM)
The topological structure of asynchronous computability
Journal of the ACM (JACM)
From binary consensus to multivalued consensus in asynchronous message-passing systems
Information Processing Letters
Wait-Free k-Set Agreement is Impossible: The Topology of Public Knowledge
SIAM Journal on Computing
The concurrency hierarchy, and algorithms for unbounded concurrency
Proceedings of the twentieth annual ACM symposium on Principles of distributed computing
The BG distributed simulation algorithm
Distributed Computing
Computing with Infinitely Many Processes
DISC '00 Proceedings of the 14th International Conference on Distributed Computing
DISC'05 Proceedings of the 19th international conference on Distributed Computing
The committee decision problem
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Anti-Ω: the weakest failure detector for set agreement
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
An impossibility about failure detectors in the iterated immediate snapshot model
Information Processing Letters
From adaptive renaming to set agreement
Theoretical Computer Science
The weakest failure detector for solving k-set agreement
Proceedings of the 28th ACM symposium on Principles of distributed computing
SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
Visiting Gafni's Reduction Land: From the BG Simulation to the Extended BG Simulation
SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
Tight group renaming on groups of size g is equivalent to g-consensus
DISC'09 Proceedings of the 23rd international conference on Distributed computing
Distributed programming with tasks
OPODIS'10 Proceedings of the 14th international conference on Principles of distributed systems
Turning adversaries into friends: simplified, made constructive, and extended
OPODIS'10 Proceedings of the 14th international conference on Principles of distributed systems
DISC'11 Proceedings of the 25th international conference on Distributed computing
| Hi-index | 0.00 |
We address the problem of solving a task T=(T1,...Tm) (called (m,1)-BG), in which a processor returns in an arbitrary one of m simultaneous consensus subtasks T1,...Tm. Processor pi submits to T an input vector of proposals (propi,1,...,propi,m), one entry per subtask, and outputs, from just one subtask ℓ, a pair (ℓ, propj,l) for some j. All processors that output at ℓ output the same proposal. Let d be a bound on the number of distinct input vectors that may be submitted to T. For example, d=3 if Democrats always vote Democrats across the board, and similarly for Republicans and Libertarians. A wait-free algorithm that immaterial of the number of processors solves T provided m ≥d is presented. In addition, if in each Tj we allow k-set consensus rather than consensus, i.e., for each ℓ, the outputs satisfy |{j | propj , ℓ}| ≤k, then the same algorithm solves T if m ≥⌈d/k ⌉. What is the power of T=(T1,...,Tm) when given as a subroutine, to be used by any number of processors with any number of input vectors? Obviously, T solves m-set consensus since each processor pi can submit the vector (idi,idi,...idi), but can m-set consensus solve T? We show it does, and thus simultaneous consensus is a new characterization of set-consensus. Finally, what if each Tj is just a binary-consensus rather than consensus? Then we get the novel problem that was recently introduced of the Committee-Decision. It was shown that for 3 processors and m=2, the simultaneous binary-consensus is equivalent to (3,2)-set consensus. Here, using a variation of our wait-free algorithms mentioned above, we show that a task, in which a processor is required to return in one of m simultaneous binary-consensus subtasks, when used by n processors, is equivalent to (n,m)-set consensus. Thus, while set-consensus unlike consensus, has no binary version, now that we characterize m-set consensus through simultaneous consensus, the notion of binary-set-consensus is well defined. We have then showed that binary-set-consensus is equivalent to set consensus as it was with consensus.