PODC '88 Proceedings of the seventh annual ACM Symposium on Principles of distributed computing
Renaming in an asynchronous environment
Journal of the ACM (JACM)
Atomic snapshots of shared memory
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
Sharing memory robustly in message-passing systems
Journal of the ACM (JACM)
Impossibility of distributed consensus with one faulty process
Journal of the ACM (JACM)
3-processor tasks are undecidable
Proceedings of the fourteenth annual ACM symposium on Principles of distributed computing
The decidability of distributed decision tasks (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of 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
Three-Processor Tasks Are Undecidable
SIAM Journal on Computing
The topological structure of asynchronous computability
Journal of the ACM (JACM)
The BG distributed simulation algorithm
Distributed Computing
New combinatorial topology upper and lower bounds for renaming
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
Subconsensus tasks: renaming is weaker than set agreement
DISC'06 Proceedings of the 20th international conference on Distributed Computing
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
Of Choices, Failures and Asynchrony: The Many Faces of Set Agreement
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
The multiplicative power of consensus numbers
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Brief announcement: on L-resilience, hitting sets, and colorless tasks
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Relating L-resilience and wait-freedom via hitting sets
ICDCN'11 Proceedings of the 12th international conference on Distributed computing and networking
A survey on some recent advances in shared memory models
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
An equivariance theorem with applications to renaming
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
Simulations and reductions for colorless tasks
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
Counting-based impossibility proofs for renaming and set agreement
DISC'12 Proceedings of the 26th international conference on Distributed Computing
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A distributed task T on n processors is an input/output relation between a collection of processors' inputs and outputs. While all tasks are solvable if no processor may ever crash, the FLP result revealed that the possibility of a failure of just a single processor precludes a solution to the task of consensus. That is consensus is not solvable 1-resiliently. Yet, some nontrivial tasks are wait-free solvable, i.e. n-1-resiliently. What tasks are solvable if at most t processors may crash? I.e. what tasks are solvable t-resiliently? The Herlihy-Shavit condition characterizes wait-free solvability, i.e., when t=n-1. The Borowsky-Gafni (BG) simulation extends this characterization to the t-resilient case for the case "colorless" tasks - tasks like consensus in which one processor can adopt the output of any other processor. It does this by reducing questions about t-resilient solvability, to a question of wait-free solvability. The latter question has been characterized. In this paper, we amend the BG-simulation to result in the Extended-BG-simulation, an extension that yields a full characterization of t-resilient solvability: A task T on n processors is solvable t-resiliently iff all tasks T' on t+1 simulators s0,..., st created as follows are wait-free solvable. Simulator si is given an input of processor pi as well as the input to a set of processors of size n-(t+1) with ids higher than i. Simulator si outputs for pi as well as for a (possibly different) set of processors of size n-(t+1) with ids higher than i. The input/output of the t+1 simulators have to be a projection of a single original input/output tuple-pair in T. We demonstrate the convenience that the characterization provides, in two ways. First, we prove a new equivalence result: We show that n processes can solve t-resiliently weak renaming with n+(t+1)-2 names, where n1 and 01 and n2, is undecidable, by a simple reduction to the undecidability of the wait-free solvability of 3-processors tasks.