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## A generalized asynchronous computability theorem

Venue: | CoRR |

Citations: | 1 - 1 self |

### Citations

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(Show Context)
Citation Context ...s, capturing the sets of possible inputs and outputs of the task. This topological characterization may provide insights about the (in)solvability of the task that are not easy to grasp operationally =-=[1, 20,30]-=-. In 1993, Herlihy and Shavit [20,21] characterized read-write communication with no restrictions on the runs; this is referred to as the wait-free model. They formulated the Asynchronous Computabilit... |

150 | The topological structure of asynchronous computability.
- Herlihy, Shavit
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(Show Context)
Citation Context ... and outputs of the task. This topological characterization may provide insights about the (in)solvability of the task that are not easy to grasp operationally [1, 20,30]. In 1993, Herlihy and Shavit =-=[20,21]-=- characterized read-write communication with no restrictions on the runs; this is referred to as the wait-free model. They formulated the Asynchronous Computability Theorem (ACT) stating that a task T... |

98 | The asynchronous computability theorem for t-resilient tasks,
- Herlihy, Shavit
- 1993
(Show Context)
Citation Context ...s, capturing the sets of possible inputs and outputs of the task. This topological characterization may provide insights about the (in)solvability of the task that are not easy to grasp operationally =-=[1, 20,30]-=-. In 1993, Herlihy and Shavit [20,21] characterized read-write communication with no restrictions on the runs; this is referred to as the wait-free model. They formulated the Asynchronous Computabilit... |

83 |
Immediate Atomic Snapshots and Fast Renaming
- Borowsky
- 1993
(Show Context)
Citation Context ...d Rajsbaum later extended this simulation to superset-closed [23] adversarial SM models [13]. However existing simulations [3, 13] combined with a multiple application of the one-shot IS construction =-=[2]-=- do not provide the desired property that a run in an SM model M casted to IIS and back remains in M . A recent paper [4] presents a two-way simulation satisfying this property and, thus, justifying t... |

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37 | A Simple Algorithmically Reasoned Characterization of Wait-free Computations
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Citation Context ...f persistent objects which can be written and read by a given process arbitrarily often. However, the original proof can be simplified by casting the problem to the iterated immediate-snapshots (IIS) =-=[3]-=- shared memory model, in which processes march through a sequence of Immediate-snapshots (IS) tasks invoking the next one with their output from the previous one. 1Computer Science Department, UCLA, 3... |

32 | A layered analysis of consensus
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(Show Context)
Citation Context ...fficulty of dealing with certain problems in certain non-compact models, such as consensus and t-resilience, has been studied before by Lubitsch and Moran [25], Brit and Moran [5], Moses and Rajsbaum =-=[26]-=-. By deriving topological solvability conditions for any task and any subIIS model, this paper brings this work to a higher level of generality. 9. Concluding remarks We presented a version of a gener... |

31 | Algebraic spans - Herlihy, Rajsbaum - 1995 |

27 |
Round-by-round fault detectors (extended abstract): unifying synchrony and asynchrony
- Gafni
- 1998
(Show Context)
Citation Context ...is always ahead of the rest (Sk = fast(r) for all k), the rest of the processes essentially proceed wait-free. In contrast, we can easily solve Lord in OF fast using commit-adopt (implemented in IIS) =-=[9]-=-. 4. Topological interpretation Recall that R denotes the set of runs in IIS. We put a metric topology on R as follows. Given runs r, r′ ∈ R, we let k = k(r, r′) denote the smallest k ≥ 0 such that th... |

24 | Three-processor tasks are undecidable - Gafni, Koutsoupias - 1999 |

24 |
and Fotios Zaharoglou. Wait-free k-set agreement is impossible: The topology of public knowledge
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(Show Context)
Citation Context ...s, capturing the sets of possible inputs and outputs of the task. This topological characterization may provide insights about the (in)solvability of the task that are not easy to grasp operationally =-=[1, 20,30]-=-. In 1993, Herlihy and Shavit [20,21] characterized read-write communication with no restrictions on the runs; this is referred to as the wait-free model. They formulated the Asynchronous Computabilit... |

13 | Subconsensus Tasks: Renaming is Weaker Than Set Agreement
- Gafni, Rajsbaum, et al.
- 2006
(Show Context)
Citation Context ...gh dimension can capture “all of distributed computing,” with respect to terminating computations. In particular, what will be the sets of runs that correspond to the availability of the Möbius task =-=[14]-=- or of a task from the family of 0-1 exclusion [10]? We know that, for instance, the symmetric task on n processes from [14] can also be formulated as a task on 2n − 1 processes, hence the increase of... |

12 | The decidability of distributed decision tasks (extended abstract - Herlihy, Rajsbaum - 1997 |

10 |
Chromatic subdivision of a simplicial complex
- Kozlov
(Show Context)
Citation Context ...less) in any (not necessarily adversarial) sub-IIS model. The IIS model was introduced by Borowsky and Gafni [3] and shown to precisely capture the standard chromatic subdivision of the input complex =-=[22,24]-=-. Due to the elegance of its topological representation, IIS has been widely used topological reasoning about distributed computing [1, 3, 15,20,21]. In [3], IIS has been shown equivalent to SM in the... |

10 | The iterated restricted immediate snapshot model
- Rajsbaum, Raynal, et al.
- 2008
(Show Context)
Citation Context ...t model by a sequence of compact models. The sequence converges to a superset of the target model. Thus, if the task is solvable by 1Some specific compact subsets of IIS runs were formally treated in =-=[29]-=-. 2 each compact model in the sequence, it is solvable by the target model. Each compact model is represented as subcomplex of a subdivided simplex. Hence GACT deals with a sub-complex of a subdivided... |

9 | The disagreement power of an adversary
- Delporte-Gallet, Fauconnier, et al.
- 2011
(Show Context)
Citation Context ...articipating sets. Given that the standard simulations [2, 3] do not meet these requirements, we employ a new two-way simulation presented in [4]. This applies to a large set of adversarial SM models =-=[7, 23]-=-, specified by sets of processes that can be infinitely participating in a model run. Thus, we can cast an adversarial SM model to its equivalent model in IIS. Moreover, the IIS model is, in a strict ... |

9 |
Distributed programming with tasks
- Gafni, Rajsbaum
- 2010
(Show Context)
Citation Context ...we translate the results back to reality. The proof of ACT in [21] can thus be simplified along the following lines: (1) The wait-free runs in standard shared-memory can be simulated in the IIS model =-=[3, 13]-=-, and the IIS model can be simulated by the standard shared-memory model [1]. Thus all we need is to characterize task solvability in IIS. (2) If a task T is wait-free solvable in the IIS model, then ... |

7 |
Closed schedulers: A novel technique for analyzing asynchronous protocols
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- 1995
(Show Context)
Citation Context ...cessarily affecting the 10 fast sets). The difficulty of dealing with certain problems in certain non-compact models, such as consensus and t-resilience, has been studied before by Lubitsch and Moran =-=[25]-=-, Brit and Moran [5], Moses and Rajsbaum [26]. By deriving topological solvability conditions for any task and any subIIS model, this paper brings this work to a higher level of generality. 9. Conclud... |

6 |
Concurrent computing and shellable complexes
- Herlihy, Rajsbaum
- 2010
(Show Context)
Citation Context ...e expressed by Herlihy and Shavit [20, 21] in the form of ACT. In the restricted case of colorless tasks that, roughly, can be defined without taking process identifiers in mind, Herlihy and Rajsbaum =-=[18,19]-=- derived task solvability conditions in adversarial shared-memory models [7], a class of SM models specified by sets of live processes. This paper proposes a characterization of generic (not necessari... |

4 | The 0-1-exclusion families of tasks
- Gafni
- 2008
(Show Context)
Citation Context ...ing,” with respect to terminating computations. In particular, what will be the sets of runs that correspond to the availability of the Möbius task [14] or of a task from the family of 0-1 exclusion =-=[10]-=-? We know that, for instance, the symmetric task on n processes from [14] can also be formulated as a task on 2n − 1 processes, hence the increase of dimension holds promise. Our speculation is that a... |

4 |
Distributed Computing Through Combinatorial Topology
- Herlihy, Kozlov, et al.
- 2014
(Show Context)
Citation Context ...ture the standard chromatic subdivision of the input complex [22,24]. Due to the elegance of its topological representation, IIS has been widely used topological reasoning about distributed computing =-=[1, 3, 15,20,21]-=-. In [3], IIS has been shown equivalent to SM in the sense that any run of IIS can simulate a run of SM in a non-blocking way, i.e., at least one fast (in IIS) process simulates infinitely many SM ste... |

3 |
Understanding non-uniform failure models. Bulletin of the European Association for Theoretical Computer
- Kuznetsov
(Show Context)
Citation Context ...articipating sets. Given that the standard simulations [2, 3] do not meet these requirements, we employ a new two-way simulation presented in [4]. This applies to a large set of adversarial SM models =-=[7, 23]-=-, specified by sets of processes that can be infinitely participating in a model run. Thus, we can cast an adversarial SM model to its equivalent model in IIS. Moreover, the IIS model is, in a strict ... |

2 | Live equals fast in iterated models
- Bouzid, Gafni, et al.
(Show Context)
Citation Context ...s [3, 13] combined with a multiple application of the one-shot IS construction [2] do not provide the desired property that a run in an SM model M casted to IIS and back remains in M . A recent paper =-=[4]-=- presents a two-way simulation satisfying this property and, thus, justifying the choice of IIS as a model of study. The IRIS model of Rajsbaum et al. [29] defines a proper subset of sub-IIS models re... |

2 | An equivariance theorem with applications to renaming - Castañeda, Herlihy, et al. - 2012 |

2 | On the wait-free power of iterated-immediate-snapshots. Unpublished manuscript, online at http: //www.cs.ucla.edu/~eli/eli/wfiis.ps
- Gafni
- 1998
(Show Context)
Citation Context ...ial tool in distributed computing [6,12,16–19]. We show that our GACT holds that promise too. We consider a task T , solvable t-resiliently, but (to our knowledge) only with a very involved algorithm =-=[8]-=-. In contrast, by applying the methods developed in this paper, we show that determining the t-resilient solvability of T is relatively simple. The paper is organized as follows: In Section 2 we descr... |

2 |
Doing the IIS. Unpublished manuscript
- Linial
- 2010
(Show Context)
Citation Context ...ucting a simplicial map from the kT -th standard chromatic subdivision of the input complex to the output complex. This is because each immediate snapshot can be represented by a standard subdivision =-=[22,24]-=-. (4) A chromatic map from an arbitrary subdivision of a complex can be approximated by a chromatic map from an iterated standard chromatic subdivision. This is a chromatic version of the standard sim... |

1 |
Wait-freedom vs. bounded-freedom in public data structures
- Brit, Moran
- 1996
(Show Context)
Citation Context ...he 10 fast sets). The difficulty of dealing with certain problems in certain non-compact models, such as consensus and t-resilience, has been studied before by Lubitsch and Moran [25], Brit and Moran =-=[5]-=-, Moses and Rajsbaum [26]. By deriving topological solvability conditions for any task and any subIIS model, this paper brings this work to a higher level of generality. 9. Concluding remarks We prese... |

1 | Free-for-all execution: Unifying resiliency, set-consensus, and concurrency. Unpublished manuscript, online at http://www.cs.ucla.edu/~eli/eli/concurrency25.pdf
- Gafni
- 2008
(Show Context)
Citation Context ...is the model in which at most t processes are slow. Example 2.3. For t ≤ n + 1, the t-obstruction-free model OF t consists of all the runs r with |fast(r)| ≤ t. This model was previously discussed in =-=[11]-=-, following a suggestion of Guerraoui. It is the model in which no more than t processes are fast. Example 2.4. More generally, consider the model with adversary A [7], which we denote by Madv(A). Her... |

1 |
The topology of distributed adversaries
- Herlihy, Rajsbaum
(Show Context)
Citation Context ...e expressed by Herlihy and Shavit [20, 21] in the form of ACT. In the restricted case of colorless tasks that, roughly, can be defined without taking process identifiers in mind, Herlihy and Rajsbaum =-=[18,19]-=- derived task solvability conditions in adversarial shared-memory models [7], a class of SM models specified by sets of live processes. This paper proposes a characterization of generic (not necessari... |