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Round-by-round fault detectors: Unifying synchrony and asynchrony
- In Proc of the 17th ACM Symp. Principles of Distributed Computing (PODC
, 1998
"... and insights. 1 Introduction For many years, researchers studying synchronous message-passing systems have considered algorithms composed of rounds of computation. In each round, a process sends a message to the others and then waits to receive messages from the other processes. The synchronous natu ..."
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Cited by 54 (9 self)
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and insights. 1 Introduction For many years, researchers studying synchronous message-passing systems have considered algorithms composed of rounds of computation. In each round, a process sends a message to the others and then waits to receive messages from the other processes. The synchronous nature of the system ensures that, by the end of the round, each process receives all messages sent to it in that round by correct processes. In the parlance of Elrad and Frances [1] then, each round of a synchronous system is a communication-closed-layer.
Hundreds of Impossibility Results for Distributed Computing
- Distributed Computing
, 2003
"... We survey results from distributed computing that show tasks to be impossible, either outright or within given resource bounds, in various models. The parameters of the models considered include synchrony, fault-tolerance, different communication media, and randomization. The resource bounds refe ..."
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Cited by 52 (5 self)
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We survey results from distributed computing that show tasks to be impossible, either outright or within given resource bounds, in various models. The parameters of the models considered include synchrony, fault-tolerance, different communication media, and randomization. The resource bounds refer to time, space and message complexity. These results are useful in understanding the inherent difficulty of individual problems and in studying the power of different models of distributed computing.
Unifying Synchronous and Asynchronous Message-Passing Models
- In Proceedings of the 17th Annual ACM Symposium on Principles of Distributed Computing
, 1998
"... We take a significant step toward unifying the synchronous, semisynchronous, and asynchronous message-passing models of distributed computation. The key idea is the concept of a pseudosphere, a new combinatorial structure in which each process from a set of processes is independently assigned a valu ..."
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Cited by 29 (11 self)
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We take a significant step toward unifying the synchronous, semisynchronous, and asynchronous message-passing models of distributed computation. The key idea is the concept of a pseudosphere, a new combinatorial structure in which each process from a set of processes is independently assigned a value from a set of values. Pseudospheres have a number of nice combinatorial properties, but their principal interest lies in the observation that the behavior of protocols in the three models can be characterized as simple unions of pseudospheres, where the exact structure of these unions is determined by the timing properties of the model. We use this pseudosphere construction to derive new and remarkably succinct proofs of bounds on consensus and k-set agreement in the asynchronous and synchronous models, as well as the first lower bound on wait-free k-set agreement in the semi-synchronous model. To appear in the 16th Annual ACM Symposium on Principles of Distributed Computing (PODC98), Puer...
Subconsensus tasks: Renaming is weaker than set agreement
- IN SHLOMI DOLEV, EDITOR, DISC, VOLUME 4167 OF LECTURE
, 2006
"... We consider the the relative power of two important synchronization problems: set agreement and renaming. We show that renaming is strictly weaker than set agreement, in a round-by-round model of computation. We introduce new techniques, including previously unknown connections between properties of ..."
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Cited by 14 (6 self)
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We consider the the relative power of two important synchronization problems: set agreement and renaming. We show that renaming is strictly weaker than set agreement, in a round-by-round model of computation. We introduce new techniques, including previously unknown connections between properties of manifolds and computation, as well as novel “symmetry-breaking” constructions.
A Simple Algorithmic Characterization of Uniform Solvability (Extended Abstract)
- Proceedings of the 43rd Annual IEEE Symposium on Foundations of Computer Science (FOCS 2002
, 2002
"... The Herlihy-Shavit (HS) conditions characterizing the solvability of asynchronous tasks over n processors have been a milestone in the development of the theory of distributed computing. Yet, they were of no help when researcher sought algorithms that do not depend on n. To help in this pursuit we i ..."
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Cited by 11 (6 self)
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The Herlihy-Shavit (HS) conditions characterizing the solvability of asynchronous tasks over n processors have been a milestone in the development of the theory of distributed computing. Yet, they were of no help when researcher sought algorithms that do not depend on n. To help in this pursuit we investigate the uniform solvability of an infinite uniform sequence of tasks T 0 , T 1 , T 2 , ..., where T i is a task over processors p 0 , p 1 , ..., p i , and T i extends T i-1 . We say that such a sequence is uniformly solvable if there exit protocols to solve each T i and the protocol for T i extends the protocol for T i-1 . This paper establishes that although each T i may be solvable, the uniform sequence is not necessarily uniformly solvable. We show this by proposing a novel uniform sequence of solvable tasks and proving that the sequence is not amenable to a uniform solution. We then extend the HS conditions for a task over n processors, to uniform solvability in a natural way. The technique we use to accomplish this is to generalize the alternative algorithmic proof, by Borowsky and Gafni, of the HS conditions, by showing that the infinite uniform sequence of task of Immediate Snapshots is uniformly solvable. A side benefit of the technique is a widely applicable methodology for the development of uniform protocols.
The Iterated Restricted Immediate Snapshot Model
, 2008
"... In the Iterated Immediate Snapshot model (IIS) the memory consists of a sequence of one-shot Immediate Snapshot (IS) objects. Processes access the sequence of IS objects, one-by-one, asynchronously, in a wait-free manner; any number of processes can crash. Its interest lies in the elegant recursive ..."
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Cited by 10 (3 self)
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In the Iterated Immediate Snapshot model (IIS) the memory consists of a sequence of one-shot Immediate Snapshot (IS) objects. Processes access the sequence of IS objects, one-by-one, asynchronously, in a wait-free manner; any number of processes can crash. Its interest lies in the elegant recursive structure of its runs, hence of the ease to analyze it round by round. In a very interesting way, Borowsky and Gafni have shown that the IIS model and the read/write model are equivalent for the wait-free solvability of decision tasks. This paper extends the benefits of the IIS model to partially synchronous systems. Given a shared memory model enriched with a failure detector, what is an equivalent IIS model? The paper shows that an elegant way of capturing the power of a failure detector and other partially synchronous systems in the IIS model is by restricting appropriately its set of runs, giving rise to the Iterated Restricted Immediate Snapshot model (IRIS).
Towards a topological characterization of asynchronous complexity
- In Proceedings of the 16th Annual ACM Symposium on Principles of Distributed Computing
, 1997
"... Abstract. This paper introduces the use of topological models and methods, formerly used to analyze computability, as tools for the quantification and classification of asynchronous complexity. We present the first asynchronous complexity theorem, applied to decision tasks in the iterated immediate ..."
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Cited by 9 (0 self)
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Abstract. This paper introduces the use of topological models and methods, formerly used to analyze computability, as tools for the quantification and classification of asynchronous complexity. We present the first asynchronous complexity theorem, applied to decision tasks in the iterated immediate snapshot (IIS) model of Borowsky and Gafni. We do so by introducing a novel form of topological tool called the nonuniform chromatic subdivision. Building on the framework of Herlihy and Shavit’s topological computability model, our theorem states that the time complexity of any asynchronous algorithm is directly proportional to the level of nonuniform chromatic subdivisions necessary to allow a simplicial map from a task’s input complex to its output complex. To show the power of our theorem, we use it to derive a new tight bound on the time to achieve n process approximate agreement in the IIS model: � max input−min input � logd, where d = 3 for two processes ɛ and d = 2 for three or more. This closes an intriguing gap between the known upper and lower bounds implied by the work of Aspnes and Herlihy. More than the new bounds themselves, the importance of our asynchronous complexity theorem is that the algorithms and lower bounds it allows us to derive are intuitive and simple, with topological proofs that require no mention of concurrency at all.
The unified structure of consensus: a layered analysis approach
- In Proceedings of the Seventeenth ACM Symposium on Principles of Distributed Computing [1
"... We introduce a simple notion of layering that provides a tool for defining submodels of a given model of distributed computation. We describe two layerings, the synchronic and the permutation layering, and show that they induce appropriate submodels of several asynchronous models of computation. The ..."
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Cited by 8 (3 self)
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We introduce a simple notion of layering that provides a tool for defining submodels of a given model of distributed computation. We describe two layerings, the synchronic and the permutation layering, and show that they induce appropriate submodels of several asynchronous models of computation. The synchronic layering applies to the synchronous model too. We perform a model-independent analysis of the consensus problem in terms of abstract connectivity properties of layering functions. By defining particular layerings in specific models, we derive several popular (and some new) lower bounds and impossibility results for consensus in various classical models. These results are often stronger in the sense that they apply to the subrnodel induced by the layering. The proofs obtained in this way are also simpler and more direct than existing ones. Moreover, the analysis is done in a uniform fashion and demonstrates the fundamental common structure of the consensus problem in the presence of failures. The analysis is then extended to general decision problems (l-resilient in the asynchronous models, t-rounds in the t-resilient synchronous model), providing a characterization of solvability of decision problems in the style of [8] which, for some of the models, is given for the first time. 1 introduction For almost two decades now, the consensus problem has played a central role in the study of fault-tolerant distributed
Lower Bounds in Distributed Computing
, 2000
"... This paper discusses results that say what cannot be computed in certain environments or when insucient resources are available. A comprehensive survey would require an entire book. As in Nancy Lynch's excellent 1989 paper, \A Hundred Impossibility Proofs for Distributed Computing" [86], w ..."
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Cited by 7 (1 self)
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This paper discusses results that say what cannot be computed in certain environments or when insucient resources are available. A comprehensive survey would require an entire book. As in Nancy Lynch's excellent 1989 paper, \A Hundred Impossibility Proofs for Distributed Computing" [86], we shall restrict ourselves to some of the results we like best or think are most important. Our aim is to give you the avour of the results and some of the techniques that have been used. We shall also mention some interesting open problems and provide an extensive list of references. The focus will be on results from the past decade.
Computable Obstructions to Wait-free Computability
- Distributed Computing
, 2000
"... Effectively computable obstructions are associated to a distributed decision task (I; O; \Delta) in the asynchronous, wait-free, read-write shared-memory model. The key new ingredient of this work is the association of a simplicial complex T , the task complex , to the input-output relation \De ..."
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Cited by 6 (2 self)
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Effectively computable obstructions are associated to a distributed decision task (I; O; \Delta) in the asynchronous, wait-free, read-write shared-memory model. The key new ingredient of this work is the association of a simplicial complex T , the task complex , to the input-output relation \Delta. The task determines a simplicial map ff from T to the input complex I. The existence of a wait-free protocol solving the task implies that the map ff induced in homology must surject, and thus elements of H (I) that are not in the image of ff are obstructions to solvability of the task. These obstructions are effectively computable when using suitable homology theories, such as mod-2 simplicial homology. We also extend Herlihy and Shavit's Theorem on Spans to the case of protocols that are anonymous relative to the action of a group, provided the action is suitably rigid . For such rigid actions, the quotients of the input complex and the task complex by the group are we...
