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The Topological Structure of Asynchronous Computability
 JOURNAL OF THE ACM
, 1996
"... We give necessary and sufficient combinatorial conditions characterizing the tasks that can be solved by asynchronous processes, of which all but one can fail, that communicate by reading and writing a shared memory. We introduce a new formalism for tasks, based on notions from classical algebra ..."
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Cited by 157 (12 self)
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We give necessary and sufficient combinatorial conditions characterizing the tasks that can be solved by asynchronous processes, of which all but one can fail, that communicate by reading and writing a shared memory. We introduce a new formalism for tasks, based on notions from classical algebraic and combinatorial topology, in which a task's possible input and output values are each associated with highdimensional geometric structures called simplicial complexes. We characterize computability in terms of the topological properties of these complexes. This characterization has a surprising geometric interpretation: a task is solvable if and only if the complex representing the task's allowable inputs can be mapped to the complex representing the task's allowable outputs by a function satisfying certain simple regularity properties. Our formalism thus replaces the "operational" notion of a waitfree decision task, expressed in terms of interleaved computations unfolding ...
Roundbyround 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 messagepassing 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 messagepassing 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 communicationclosedlayer.
Algebraic spans
, 2000
"... Topological methods have yielded a variety of lower bounds and impossibility results for distributed computing. In this paper, we introduce a new tool for proving impossibility results, which is based on a core theorem of algebraic topology, the acyclic carrier theorem, and unifies, generalizes and ..."
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Cited by 35 (17 self)
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Topological methods have yielded a variety of lower bounds and impossibility results for distributed computing. In this paper, we introduce a new tool for proving impossibility results, which is based on a core theorem of algebraic topology, the acyclic carrier theorem, and unifies, generalizes and extends earlier results.
Set Consensus Using Arbitrary Objects
 In Proceedings of the thirteenth annual ACM symposium on Principles of distributed computing
, 1994
"... In the (N; k)consensus task, each process in a group starts with a private input value, communicates with the others by applying operations to shared objects, and then halts after choosing a private output value. Each process is required to choose some process's input value, and the set of val ..."
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Cited by 34 (17 self)
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In the (N; k)consensus task, each process in a group starts with a private input value, communicates with the others by applying operations to shared objects, and then halts after choosing a private output value. Each process is required to choose some process's input value, and the set of values chosen should have size at most k. This problem, first proposed by Chaudhuri in 1990, has been extensively studied using asynchronous read/write memory. In this paper, we investigate this problem in a more powerful asynchronous model in which processes may communicate through objects other than read/write memory, such as test&set variables. We prove two general theorems about the solvability of set consensus using objects other than read/write registers. The first theorem addresses the question of what kinds of shared objects are needed to solve (N; k)consensus, and the second addresses the question of what kinds of tasks can be solved by N processes using (M; j)consensus objects, for M N...
Unifying Synchronous and Asynchronous MessagePassing 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 messagepassing 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 messagepassing 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 kset agreement in the asynchronous and synchronous models, as well as the first lower bound on waitfree kset agreement in the semisynchronous model. To appear in the 16th Annual ACM Symposium on Principles of Distributed Computing (PODC98), Puer...
The Combinatorial Structure of Waitfree Solvable Tasks (Extended Abstract)
, 1996
"... This paper presents a selfcontained study of waitfree solvable tasks. A new necessary and sufficient condition for waitfree solvability is proved, providing a characterization of the waitfree solvable tasks. The necessary condition is used to prove tight bounds on renaming and kset consensus. ..."
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Cited by 25 (14 self)
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This paper presents a selfcontained study of waitfree solvable tasks. A new necessary and sufficient condition for waitfree solvability is proved, providing a characterization of the waitfree solvable tasks. The necessary condition is used to prove tight bounds on renaming and kset consensus. The framework is based on topology, but uses only elementary combinatorics, and does not rely on algebraic or geometric arguments.
A Tutorial on Algebraic Topology and Distributed Computation
 Lecture Notes in Computer Science
, 1994
"... This document is a set of course notes from an informal tutorial to be presented at UCLA in August 1994. These notes are intended to be informative, even provocative, but are not intended to be balanced, comprehensive, or authoritative. All reasonable suggestions for improvement will be enthusiastic ..."
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Cited by 16 (2 self)
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This document is a set of course notes from an informal tutorial to be presented at UCLA in August 1994. These notes are intended to be informative, even provocative, but are not intended to be balanced, comprehensive, or authoritative. All reasonable suggestions for improvement will be enthusiastically acknowledged in future revisions. 1 Introduction
Algebraic Topology and Distributed Computing A Primer
, 1995
"... . Models and techniques borrowed from classical algebraic topology have recently yielded a variety of new lower bounds and impossibility results for distributed and concurrent computation. This paper explains the basic concepts underlying this approach, and shows how they apply to a simple distribut ..."
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Cited by 12 (0 self)
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. Models and techniques borrowed from classical algebraic topology have recently yielded a variety of new lower bounds and impossibility results for distributed and concurrent computation. This paper explains the basic concepts underlying this approach, and shows how they apply to a simple distributed problem. 1 Introduction The problem of coordinating concurrent processes remains one of the central problems of distributed computing. Coordination problems arise at all scales in distributed and concurrent systems, ranging from synchronizing data access in tightlycoupled multiprocessors, to allocating data paths in networks. Coordination is difficult because modern multiprocessor systems are inherently asynchronous: processes may be delayed without warning for a variety of reasons, including interrupts, preemption, cache misses, communication delays, or failures. These delays can vary enormously in scale: a cache miss might delay a process for fewer than ten instructions, a page fault...
Time Bounds for Decision Problems in the Presence of Timing Uncertainty and Failures
 Journal of Parallel and Distributed Computing
, 1993
"... This paper studies the time complexity of solving decision problems in ..."
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Cited by 11 (2 self)
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This paper studies the time complexity of solving decision problems in
Of Choices, Failures and Asynchrony: The Many Faces of Set Agreement
"... Abstract. Set agreement is a fundamental problem in distributed computing in which processes collectively choose a small subset of values from a larger set of proposals. The impossibility of faulttolerant set agreement in asynchronous networks is one of the seminal results in distributed computing. ..."
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Cited by 8 (4 self)
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Abstract. Set agreement is a fundamental problem in distributed computing in which processes collectively choose a small subset of values from a larger set of proposals. The impossibility of faulttolerant set agreement in asynchronous networks is one of the seminal results in distributed computing. The complexity of set agreement in synchronous networks has also been a significant research challenge. Real systems, however, are neither purely synchronous nor purely asynchronous. Rather, they tend to alternate between periods of synchrony and periods of asynchrony. In this paper, we analyze the complexity of set agreement in a such a “partially synchronous ” setting, presenting the first (asymptotically) tight bound on the complexity of set agreement in such systems. We introduce a novel technique for simulating, in faultprone asynchronous shared memory, executions of an asynchronous and failureprone messagepassing system in which some fragments appear synchronous to some processes. We use this technique to derive a lower bound on the round complexity of set agreement in a partially synchronous system by a reduction from asynchronous waitfree set agreement. We also present an asymptotically matching algorithm that relies on a distributed asynchrony detection mechanism to decide as soon as possible during periods of synchrony. By relating environments with differing degrees of synchrony, our simulation technique is of independent interest. In particular, it allows us to obtain a new lower bound on the complexity of early deciding kset agreement complementary to that of [12], and to rederive the combinatorial topology lower bound of [13] in an algorithmic way. 1