Impossibility of distributed consensus with one faulty process
TL;DR: In this paper, it is shown that every protocol for this problem has the possibility of nontermination, even with only one faulty process.
Abstract: The consensus problem involves an asynchronous system of processes, some of which may be unreliable The problem is for the reliable processes to agree on a binary value In this paper, it is shown that every protocol for this problem has the possibility of nontermination, even with only one faulty process By way of contrast, solutions are known for the synchronous case, the “Byzantine Generals” problem
Citations
More filters
Book•
01 Jan 1996
TL;DR: This book familiarizes readers with important problems, algorithms, and impossibility results in the area, and teaches readers how to reason carefully about distributed algorithms-to model them formally, devise precise specifications for their required behavior, prove their correctness, and evaluate their performance with realistic measures.
Abstract: In Distributed Algorithms, Nancy Lynch provides a blueprint for designing, implementing, and analyzing distributed algorithms. She directs her book at a wide audience, including students, programmers, system designers, and researchers.
Distributed Algorithms contains the most significant algorithms and impossibility results in the area, all in a simple automata-theoretic setting. The algorithms are proved correct, and their complexity is analyzed according to precisely defined complexity measures. The problems covered include resource allocation, communication, consensus among distributed processes, data consistency, deadlock detection, leader election, global snapshots, and many others.
The material is organized according to the system model-first by the timing model and then by the interprocess communication mechanism. The material on system models is isolated in separate chapters for easy reference.
The presentation is completely rigorous, yet is intuitive enough for immediate comprehension. This book familiarizes readers with important problems, algorithms, and impossibility results in the area: readers can then recognize the problems when they arise in practice, apply the algorithms to solve them, and use the impossibility results to determine whether problems are unsolvable. The book also provides readers with the basic mathematical tools for designing new algorithms and proving new impossibility results. In addition, it teaches readers how to reason carefully about distributed algorithms-to model them formally, devise precise specifications for their required behavior, prove their correctness, and evaluate their performance with realistic measures.
Table of Contents
1 Introduction
2 Modelling I; Synchronous Network Model
3 Leader Election in a Synchronous Ring
4 Algorithms in General Synchronous Networks
5 Distributed Consensus with Link Failures
6 Distributed Consensus with Process Failures
7 More Consensus Problems
8 Modelling II: Asynchronous System Model
9 Modelling III: Asynchronous Shared Memory Model
10 Mutual Exclusion
11 Resource Allocation
12 Consensus
13 Atomic Objects
14 Modelling IV: Asynchronous Network Model
15 Basic Asynchronous Network Algorithms
16 Synchronizers
17 Shared Memory versus Networks
18 Logical Time
19 Global Snapshots and Stable Properties
20 Network Resource Allocation
21 Asynchronous Networks with Process Failures
22 Data Link Protocols
23 Partially Synchronous System Models
24 Mutual Exclusion with Partial Synchrony
25 Consensus with Partial Synchrony
4,340 citations
01 Jan 2000
TL;DR: This article briefly reviews the basic concepts about cognitive radio CR, and the need for software-defined radios is underlined and the most important notions used for such.
Abstract: An Integrated Agent Architecture for Software Defined Radio. Rapid-prototype cognitive radio, CR1, was developed to apply these.The modern software defined radio has been called the heart of a cognitive radio. Cognitive radio: an integrated agent architecture for software defined radio. Http:bwrc.eecs.berkeley.eduResearchMCMACR White paper final1.pdf. The cognitive radio, built on a software-defined radio, assumes. Radio: An Integrated Agent Architecture for Software Defined Radio, Ph.D. The need for software-defined radios is underlined and the most important notions used for such. Mitola III, Cognitive radio: an integrated agent architecture for software defined radio, Ph.D. This results in the set-theoretic ontology of radio knowledge defined in the. Cognitive Radio An Integrated Agent Architecture for Software.This article first briefly reviews the basic concepts about cognitive radio CR. Cognitive Radio-An Integrated Agent Architecture for Software Defined Radio. Cognitive Radio RHMZ 2007. Software-defined radio SDR idea 1. Cognitive radio: An integrated agent architecture for software.Cognitive Radio SOFTWARE DEFINED RADIO, AND ADAPTIVE WIRELESS SYSTEMS2 Cognitive Networks. 3 Joseph Mitola III, Cognitive Radio: An Integrated Agent Architecture for Software Defined Radio Stockholm.
3,814 citations
22 Feb 1999
TL;DR: A new replication algorithm that is able to tolerate Byzantine faults that works in asynchronous environments like the Internet and incorporates several important optimizations that improve the response time of previous algorithms by more than an order of magnitude.
Abstract: This paper describes a new replication algorithm that is able to tolerate Byzantine faults. We believe that Byzantinefault-tolerant algorithms will be increasingly important in the future because malicious attacks and software errors are increasingly common and can cause faulty nodes to exhibit arbitrary behavior. Whereas previous algorithms assumed a synchronous system or were too slow to be used in practice, the algorithm described in this paper is practical: it works in asynchronous environments like the Internet and incorporates several important optimizations that improve the response time of previous algorithms by more than an order of magnitude. We implemented a Byzantine-fault-tolerant NFS service using our algorithm and measured its performance. The results show that our service is only 3% slower than a standard unreplicated NFS.
3,562 citations
TL;DR: The Paxon parliament's protocol provides a new way of implementing the state machine approach to the design of distributed systems.
Abstract: Recent archaeological discoveries on the island of Paxos reveal that the parliament functioned despite the peripatetic propensity of its part-time legislators. The legislators maintained consistent copies of the parliamentary record, despite their frequent forays from the chamber and the forgetfulness of their messengers. The Paxon parliament's protocol provides a new way of implementing the state machine approach to the design of distributed systems.
2,965 citations
01 Jan 1989
TL;DR: The focus is on the qualitative aspects of control, but computation and the related issue of computational complexity are also considered.
Abstract: A discrete event system (DES) is a dynamic system that evolves in accordance with the abrupt occurrence, at possibly unknown irregular intervals, of physical events. Such systems arise in a variety of contexts ranging from computer operating systems to the control of complex multimode processes. A control theory for the logical aspects of such DESs is surveyed. The focus is on the qualitative aspects of control, but computation and the related issue of computational complexity are also considered. Automata and formal language models for DESs are surveyed. >
2,829 citations
References
More filters
TL;DR: The Albanian Generals Problem as mentioned in this paper is a generalization of Dijkstra's dining philosophers problem, where two generals have to come to a common agreement on whether to attack or retreat, but can communicate only by sending messengers who might never arrive.
Abstract: I have long felt that, because it was posed as a cute problem about philosophers seated around a table, Dijkstra’s dining philosopher’s problem received much more attention than it deserves. (For example, it has probably received more attention in the theory community than the readers/writers problem, which illustrates the same principles and has much more practical importance.) I believed that the problem introduced in [41] was very important and deserved the attention of computer scientists. The popularity of the dining philosophers problem taught me that the best way to attract attention to a problem is to present it in terms of a story. There is a problem in distributed computing that is sometimes called the Chinese Generals Problem, in which two generals have to come to a common agreement on whether to attack or retreat, but can communicate only by sending messengers who might never arrive. I stole the idea of the generals and posed the problem in terms of a group of generals, some of whom may be traitors, who have to reach a common decision. I wanted to assign the generals a nationality that would not offend any readers. At the time, Albania was a completely closed society, and I felt it unlikely that there would be any Albanians around to object, so the original title of this paper was The Albanian Generals Problem. Jack Goldberg was smart enough to realize that there were Albanians in the world outside Albania, and Albania might not always be a black hole, so he suggested that I find another name. The obviously more appropriate Byzantine generals then occurred to me. The main reason for writing this paper was to assign the new name to the problem. But a new paper needed new results as well. I came up with a simpler way to describe the general 3n+1-processor algorithm. (Shostak’s 4-processor algorithm was subtle but easy to understand; Pease’s generalization was a remarkable tour de force.) We also added a generalization to networks that were not completely connected. (I don’t remember whose work that was.) I also added some discussion of practical implementation details.
5,208 citations
TL;DR: In this article, a group of generals of the Byzantine army camped with their troops around an enemy city are shown to agree upon a common battle plan using only oral messages, if and only if more than two-thirds of the generals are loyal; so a single traitor can confound two loyal generals.
Abstract: Reliable computer systems must handle malfunctioning components that give conflicting information to different parts of the system. This situation can be expressed abstractly in terms of a group of generals of the Byzantine army camped with their troops around an enemy city. Communicating only by messenger, the generals must agree upon a common battle plan. However, one or more of them may be traitors who will try to confuse the others. The problem is to find an algorithm to ensure that the loyal generals will reach agreement. It is shown that, using only oral messages, this problem is solvable if and only if more than two-thirds of the generals are loyal; so a single traitor can confound two loyal generals. With unforgeable written messages, the problem is solvable for any number of generals and possible traitors. Applications of the solutions to reliable computer systems are then discussed.
4,901 citations
TL;DR: It is shown that the problem is solvable for, and only for, n ≥ 3m + 1, where m is the number of faulty processors and n is the total number and this weaker assumption can be approximated in practice using cryptographic methods.
Abstract: The problem addressed here concerns a set of isolated processors, some unknown subset of which may be faulty, that communicate only by means of two-party messages. Each nonfaulty processor has a private value of information that must be communicated to each other nonfaulty processor. Nonfaulty processors always communicate honestly, whereas faulty processors may lie. The problem is to devise an algorithm in which processors communicate their own values and relay values received from others that allows each nonfaulty processor to infer a value for each other processor. The value inferred for a nonfaulty processor must be that processor's private value, and the value inferred for a faulty one must be consistent with the corresponding value inferred by each other nonfaulty processor.It is shown that the problem is solvable for, and only for, n ≥ 3m + 1, where m is the number of faulty processors and n is the total number. It is also shown that if faulty processors can refuse to pass on information but cannot falsely relay information, the problem is solvable for arbitrary n ≥ m ≥ 0. This weaker assumption can be approximated in practice using cryptographic methods.
2,457 citations
TL;DR: This paper discusses elections and reorganizations of active nodes in a distributed computing system after a failure, and two types of reasonable failure environments are studied.
Abstract: After a failure occurs in a distributed computing system, it is often necessary to reorganize the active nodes so that they can continue to perform a useful task. The first step in such a reorganization or reconfiguration is to elect a coordinator node to manage the operation. This paper discusses such elections and reorganizations. Two types of reasonable failure environments are studied. For each environment assertions which define the meaning of an election are presented. An election algorithm which satisfies the assertions is presented for each environment.
647 citations
07 Nov 1983
TL;DR: A randomized solution for the Byzantine Generals Problems that produces Byzantine Agreement within a fixed small expected number of computational rounds, independent of the number n of processes and the bound t on the number of faulty processes.
Abstract: We present a randomized solution for the Byzantine Generals Problems. The solution works in the synchronous as well as the asynchronous case and produces Byzantine Agreement within a fixed small expected number of computational rounds, independent of the number n of processes and the bound t on the number of faulty processes. The solution uses A. Shamir's method for sharing secrets. It specializes to produce a simple solution for the Distributed Commit problem.
620 citations