Renaming in an asynchronous environment
Journal of the ACM (JACM)
Impossibility results for asynchronous PRAM (extended abstract)
SPAA '91 Proceedings of the third annual ACM symposium on Parallel algorithms and architectures
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
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
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
A direct lower bound for k-set consensus
PODC '98 Proceedings of the seventeenth annual ACM symposium on Principles of distributed computing
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
The BG distributed simulation algorithm
Distributed Computing
The Combinatorial Structure of Wait-Free Solvable Tasks
SIAM Journal on Computing
A Layered Analysis of Consensus
SIAM Journal on Computing
Polynominal and Adaptive Long-Lived (2k-1)-Renaming
DISC '00 Proceedings of the 14th International Conference on Distributed Computing
Mathematical Structures in Computer Science
Distributed Computing: Fundamentals, Simulations and Advanced Topics
Distributed Computing: Fundamentals, Simulations and Advanced Topics
PRDC '06 Proceedings of the 12th Pacific Rim International Symposium on Dependable Computing
New combinatorial topology upper and lower bounds for renaming
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
The 0---1-Exclusion Families of Tasks
OPODIS '08 Proceedings of the 12th International Conference on Principles of Distributed Systems
The extended BG-simulation and the characterization of t-resiliency
Proceedings of the forty-first annual ACM symposium on Theory of computing
Recursion in distributed computing
SSS'10 Proceedings of the 12th international conference on Stabilization, safety, and security of distributed systems
The universe of symmetry breaking tasks
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
A non-topological proof for the impossibility of k-set agreement
SSS'11 Proceedings of the 13th international conference on Stabilization, safety, and security of distributed systems
ICDCN'06 Proceedings of the 8th international conference on Distributed Computing and Networking
New combinatorial topology bounds for renaming: The upper bound
Journal of the ACM (JACM)
Subconsensus tasks: renaming is weaker than set agreement
DISC'06 Proceedings of the 20th international conference on Distributed Computing
An equivariance theorem with applications to renaming
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
The renaming problem in shared memory systems: An introduction
Computer Science Review
Randomized loose renaming in o(log log n) time
Proceedings of the 2013 ACM symposium on Principles of distributed computing
Upper bound on the complexity of solving hard renaming
Proceedings of the 2013 ACM symposium on Principles of distributed computing
A non-topological proof for the impossibility of k-set agreement
Theoretical Computer Science
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Renaming and set agreement are two fundamental sub-consensus tasks. In the M-renaming task, processes start with names from a large domain and must decide on distinct names in a range of size M; in the k-set agreement task, processes must decide on at most k of their input values. Renaming and set agreement are representatives of the classes of colored and colorless tasks, respectively. This paper presents simple proofs for key impossibility results for wait-free computation using only read and write operations: n processes cannot solve (n−1)-set agreement, and, if n is a prime power, n processes cannot solve (2n−2)-renaming. Our proofs consider a restricted set of executions, and combine simple operational properties of these executions with elementary counting arguments, to show the existence of an execution violating the task's requirements. This makes the proofs easier to understand, verify, and hopefully, extend.