Consensus In Asynchronous Systems Research Articles

Consensus using omega in asynchronous systems with unknown membership and degenerative Byzantine failures

We study consensus in asynchronous systems where membership is unknown, and where up to f degenerative Byzantine failures can happen. In our failure model a faulty process can have a Byzantine behavior (i.e., it deviates from its specification), and, furthermore, every faulty process will degenerate such that eventually it will have permanent physical or transmission failures. We present a simple algorithm that solves Consensus using the Omega failure detector and a new broadcast primitive called RFLOB in an asynchronous system with degenerative Byzantine failures, which is optimal with respect to failures because it works when f<n/3. RFLOB guarantees reliable, FIFO and local order broadcast in systems with Byzantine processes and unknown membership. Finally, we present an algorithm that implements an Omega failure detector with unknown membership and minimum connectivity (i.e., communication reliability, and synchrony properties) in a system with degenerative Byzantine failures.

A weakly-adaptive condition-based consensus algorithm in asynchronous distributed systems

The consensus problem is one of the most fundamental and important problems for designing fault-tolerant distributed systems. In the consensus problem, each process proposes a value, and all non-faulty processes have to agree on a common value that is proposed by a process. Despite of many applications (e.g., atomic broadcast [2, 6], shared object [1, 7], weak atomic commitment [5]), it is known that the consensus problem has no deterministic solution in asynchronous systems subject to only a single crash fault [4]. Thus, to circumvent this impossibility, several approaches, such as partial synchrony [3] and unreliable failure detectors [2], have been proposed. As one of such approaches, the condition-based approach is recently introduced [9]. This approach introduces restriction (called condition) on inputs so that the generally-unsolvable problem can be solved for the restricted set of inputs. In the case of the consensus problem, a condition is defined as a subset of all possible input vectors whose entries correspond to the proposal of each process. The first result of the condition-based approach clarifies the condition for which the uniform consensus can be solved in asynchronous systems subject to crash faults [9]. This result proposed a class of conditions, called t-legal conditions, and proved that the t-legal conditions form the class of necessary and sufficient conditions to solve the consensus in asynchronous systems where at most t process can crash. In general, for smaller number of t, the t-legal conditions become weaker restrictions and can contain more input vectors. An example of such t-legal conditions is the condition Cmax t , proposed in [9]. The condition Cmax t is the set of input vectors where the maximum value in each vector appears at t entries or more in the vector. From the definition, the condition Cmax t is a subset of the condition Cmax t−1 . In this sense, the sizes of sufficient conditions are strongly related to the number of crash faults that the system suffers. That is, the consensus algorithm designed for tolerating a larger number of faults can solve the consensus problem only for a smaller set of input vectors. However, in the system with t crash faults at a maximum, it is not often that t processes actually crashes. In other words, the actual number of crash faults is relatively smaller than the maximum. This observation brings one question as follows: Can we construct the condition-based algorithm that solves the consensus problem for more relaxed conditions than t-legal one when the actual number of crash faults is smaller than t ? In this paper, we investigate this problem by applying the adaptive condition-based approach. In the adaptive condition-based approach, a restriction to input vectors is not represented by a single subset of inputs, but represented by a hierarchical sequence of conditions called a condition sequence. Adaptive condition-based algorithms are instantiated by a condition sequence, and guarantee some property according to the position of input vector in the hierarchy of the given condition sequence (i.e., the execution for the input vector with higher position achieves better property). The first result for the adaptive condition-based approach considers time complexity in the synchronous

Illustrating the impossibility of crash-tolerant consensus in asynchronous systems

This exercise shows how a simple restricted algorithm can be used to present an introductory discussion on the crash-tolerant consensus problem in asynchronous distributed systems. This text is intended to support teaching the consensus problem in courses on distributed systems.

Failure detection and consensus in the crash-recovery model

We study the problems of failure detection and consensus in asynchronous systems in which processes may crash and recover, and links may lose messages. We first propose new failure detectors that are particularly suitable to the crash-recovery model. We next determine under what conditions stable storage is necessary to solve consensus in this model. Using the new failure detectors, we give two consensus algorithms that match these conditions: one requires stable storage and the other does not. Both algorithms tolerate link failures and are particularly efficient in the runs that are most likely in practice - those with no failures or failure detector mistakes. In such runs, consensus is achieved within 3δ time and with 4n messages, where δ is the maximum message delay and n is the number of processes in the system.

A simple and fast asynchronous consensus protocol based on a weak failure detector

The Consensus problem is a fundamental paradigm for fault-tolerant asynchronous systems. It abstracts a family of problems known as Agreement (or Coordination) problems. Any solution to consensus can serve as a basic building block for solving such problems (e.g., atomic commitment or atomic broadcast). Solving consensus in an asynchronous system is not a trivial task: it has been proven (1985) by Fischer, Lynch and Paterson that there is no deterministic solution in asynchronous systems which are subject to even a single crash failure. To circumvent this impossibility result, Chandra and Toueg have introduced the concept of unreliable failure detectors (1991), and have studied how these failure detectors can be used to solve consensus in asynchronous systems with crash failures. This paper presents a new consensus protocol that uses a failure detector of the class $\Diamond{\cal S}$ . Like previous protocols, it is based on the rotating coordinator paradigm and proceeds in asynchronous rounds. Simplicity and efficiency are the main characteristics of this protocol. From a performance point of view, the protocol is particularly efficient when, whether failures occur or not, the underlying failure detector makes no mistake (a common case in practice). From a design point of view, the protocol is based on the combination of three simple mechanisms: a voting mechanism, a small finite state automaton which manages the behavior of each process, and the possibility for a process to change its mind during a round.

Failure Detection and Randomization: A Hybrid Approach to Solve Consensus

We present a consensus algorithm that combines unreliable failure detection and randomization, two well-known techniques for solving consensus in asynchronous systems with crash failures. This hybrid algorithm combines advantages from both approaches: it guarantees deterministic termination if the failure detector is accurate, and probabilistic termination otherwise. In executions with no failures or failure detector mistakes, the most likely ones in practice, consensus is reached in only two asynchronous rounds.

The weakest failure detector for solving consensus

We determine what information about failures is necessary and sufficient to solve Consensus in asynchronous distributed systems subject to crash failures. In Chandra and Toueg [1996], it is shown thatW, a failure detector that provides surprisingly little information about which processes have crashed, is sufficient to solve Consensus in asynchronous systems with a majority of correct processes. In this paper, we prove that to solve Consensus, any failure detector has to provide at least as much information as W. Thus, W is indeed the weakest failure detector for solving Consensus in asynchronous systems with a majority of correct processes.

Unreliable failure detectors for reliable distributed systems

We introduce the concept of unreliable failure detectors and study how they can be used to solve Consensus in asynchronous systems with crash failures. We characterise unreliable failure detectors in terms of two properties—completeness and accuracy. We show that Consensus can be solved even with unreliable failure detectors that make an infinite number of mistakes, and determine which ones can be used to solve Consensus despite any number of crashes, and which ones require a majority of correct processes. We prove that Consensus and Atomic Broadcast are reducible to each other in asynchronous systems with crash failures; thus, the above results also apply to Atomic Broadcast. A companion paper shows that one of the failure detectors introduced here is the weakest failure detector for solving Consensus [Chandra et al. 1992].