Faulty Processors Research Articles

The new territory of mobile agreement

The fault-tolerance is an important research topic in the study of distributed systems. To cope with the influence from faulty processors, reaching a common agreement at the presence of faults before performing some special tasks is essential. Therefore, the Byzantine Agreement (BA) problem has drawn more and more of the researchers' attention as they explore deeper and deeper into the world of distributed systems. Traditionally, the BA problem is solved in the fully connected network or in the broadcast network. However, the technology of network continues to grow at high-speed, it promotes the wireless and mobile computer to become increasingly popular. It can also provide support for mobile computing. This environment encourages distributed system design and practice to support mobile processors greatly. The mobile network is different from the fully connected network or broadcast network; processors in mobile environment have high mobility. The processors may immigrate into or move away from the network at any time. How the processors reach an agreement in the mobile network must also be concerned deeply. In this paper, BA problem is reexamined under the mobile network. The proposed protocol Byzantine Agreement under Mobile Network (BAMN) uses the minimum number of message exchanges to reach an agreement while tolerating the maximum number of faulty processors in a mobile environment. It makes all the healthy processors reach a common value to keep the system from the influences of processor failures.

On Locating-Dominating Codes in Binary Hamming Spaces

Locating faulty processors in a multiprocessor system gives the motivation for locating-dominating codes. We consider these codes in binary hypercubes and generalize the concept for the situation in which we want to locate more than one malfunctioning processor.

Resilient-optimal interactive consistency in constant time

For a complete network of n processors within which communication lines are private, we show how to achieve concurrently many Byzantine Agreements within constant expected time both on synchronous and asynchronous networks. As an immediate consequence, this provides a solution to the Interactive Consistency problem. Our algorithms tolerate up to (n - 1)/3 faulty processors in both the synchronous and asynchronous cases and are therefore resilient-optimal.In terms of time complexity, our results improve a time bound of O(log n) (for n concurrent agreements) which is immediately implied by the constant expected time Byzantine Agreement of Feldman and Micali (synchronous systems) and of Canetti and Rabin (asynchronous systems). In terms of resiliency, our results improve the resiliency bound of the constant time, O(4√n)-resilient algorithm of Ben-Or.An immediate application of our protocols is a constant expected time simulation of simultaneous broadcast channels over a network with private lines.

Reaching agreement on an unknown network with partial graphic information

The Byzantine Agreement (BA) is an important topic in the reliable distributed system because the system can cope with the influences from faulty components when the agreement is achieved. In the literature concerned, the BA problem has been well formulated in a Fully Connected Network (FCN) and a Generalized Connected Network (GCN) under the assumption that each processor in the network has the common knowledge of the graphic information about the entire network structure. However, in the real world, each processor may not have the common knowledge of the graphic information about the entire network structure. That is, the processors may only have the partial knowledge as to their own graphic information. In this paper, the Byzantine Agreement problem will be visited in an Unknown Network (UNet) to increase the capability of fault tolerance by allowing faulty processors with dual failure mode. The proposed protocols, the Unknown Agreement Protocol (UAP) and the Relay Channel (RC), use the minimum number of rounds of message exchange and can tolerate the maximum number of faulty processors allowed.

Asynchronous consensus protocol for the unreliable un-fully connected network

In order to achieve reliability in the distributed system, we need a mechanism to enable the system as a whole to continue to function despite the system has some faulty components. The Consensus problem is for the fault-free processors to cope with the faulty components and reach a common value from each other in the distributed system. Traditionally, the Consensus problems were solved in the synchronous network. Subsequently, Chandra and Toueg solved the Consensus problem with crash faulty processor in the asynchronous fully connected network in 1996. In this paper, we will solve the Consensus with dual failure mode (both crash fault and malicious fault) on communication links. The proposed protocol uses the minimum number of rounds of message exchange and can tolerate the maximum number of allowable faulty communication links to make each fault-free processor reach a common consensus value.

On the Identification of Sets of Points in the Square Lattice

Abstract. Identifying codes in the square lattice are considered. The motivation for these codes is the following: if a multiprocessor system is modelled by the square lattice, then we can locate faulty processors in the system with the aid of identifying codes. Constructions, some of which are optimal, are given.

Families of optimal codes for strong identification

Codes for strong identification are considered. The motivation for these codes comes from locating faulty processors in a multiprocessor system. Constructions and lower bounds on these codes are given. In particular, we provide two infinite families of optimal strongly identifying codes, which can locate up to two malfunctioning processors in a binary hypercube.

Two families of optimal identifying codes in binary Hamming spaces

A motivation for identifying codes comes from quality control in multiprocessor systems, that is, we are able, with the aid of these codes, to find faulty processors in such a system. We give a construction of two infinite families of optimal codes, which identify up to two malfunctioning processors in Hamming spaces.

Sequences of optimal identifying codes

Locating faulty processors in a multiprocessor system gives the motivation for identifying codes. Denote by l the maximum number of simultaneously malfunctioning processors. We show that if l/spl ges/3, then the problem of finding the smallest cardinality of a (1, /spl les/l)-identifying code in a binary hypercube is equivalent to the problem of finding the smallest size of a (2l-1)-fold 1-covering. This observation yields infinite sequences of optimal identifying codes for every l (l/spl ges/3).

An evolutionary algorithm for generalized comparison-based self-diagnosis of multiprocessor systems

In this article, we consider the problem of self-diagnosis of multiprocessor and multicomputer systems under the generalized comparison model. In this approach, a system consists of a collection n independent heterogeneous processors (or units) interconnected via point-to-point communication links, and it is assumed that at most t of these processors are permanently faulty. For the purpose of diagnosis, system tasks are assigned to pairs of processors and the results are compared. The agreements and disagreements among units are the basis for identifying faulty processors. Such a system is said to be t-diagnosable if, given any complete collection of comparison results, the set of faulty processors can be unambiguously identified. We present an efficient fault identification method based on genetic algorithms. Analysis and simulations are provided, first, to evaluate the genetic parameters of the diagnosis algorithm; second, to show the efficiency of the genetic approach. The new strategy is shown to correctly identify the set of faulty processors, making it an attractive and viable addition or alternative to present fault diagnosis techniques.

On strongly identifying codes

Identifying codes are designed for locating faulty processors in multiprocessor systems. In this paper we consider a natural extension of this problem and introduce strongly identifying codes. Several lower bounds and constructions are given and relations between different types of identifying codes are examined.

Evaluation of Fault-Tolerant Multiprocessor Systems for High Assurance Applications

In designing high assurance systems, the dependability goals are achieved through the adoption of several fault tolerance techniques. Unfortunately, their combined effect on the system cannot be, in the general case, derived by straightforward composition of the stand-alone component's analysis, because of mutual dependence of their controlling parameters. In this paper the assessment of overall system dependability induced by such integrated fault tolerance organizations is carried out through a stochastic simulation approach. To this purpose, a few fault tolerant multiprocessor architectures, based on the integrated usage of standard error processing structures with a recently proposed diagnostic mechanism, called -count, are selected and evaluated. The diagnostic mechanism gets its input (error signals) from the error processing mechanism, whose behaviour is in turn influenced by the rapidity and correctness with which -count identifies permanently/intermittently faulty processors. The choice of the basic fault tolerance mechanisms to adopt, as well as the reference system architecture, has been driven by the characteristics of the envisaged target applications: mainly, stringent dependability requirements, to be traded with adequate levels of performance and cost. The analysis has been focused on performability, which is an appropriate measure to evaluate whether a certain design is better than another under dependability and performance point of view.

Codes for Strong Identification

Abstract Identifying codes are designed for locating faulty processors in multiprocessor systems. In this paper we consider a natural extension of this problem and introduce strongly identifying codes. Lower bounds and constructions are given and relations between different types of identifying codes are examined.

Correct and almost complete diagnosis of processor grids

A new diagnosis algorithm for square grids is introduced. The algorithm always provides correct diagnosis if the number of faulty processors is below T, a bound with T /spl epsi//spl Theta/(n/sup 2/3/), which was derived by worst-case analysis. A more effective tool to validate the diagnosis correctness is the syndrome dependent bound T/sub /spl sigma// with T/sub /spl sigma///spl ges/T, asserted by the diagnosis algorithm itself for every given diagnosis experiment. Simulation studies provided evidence that the diagnosis is complete or almost complete if the number of faults is below T. The fraction of units which cannot be identified as either faulty or nonfaulty remains relatively small as long as the number of faults is below n/3 and, as long as the number of faults is below n/2, the diagnosis is correct with high probability.

Fully Scalable Fault-Tolerant Simulations for BSP and CGM

In this paper we consider general simulations of algorithms designed for fully operational BSP and CGM machines on machines with faulty processors. The BSP (or CGM) machine is a parallel multicomputer consisting of p processors for which a memory of n words is evenly distributed and each processor can send and receive at most h messages in a superstep. The faults are deterministic (i.e., worst-case distributions of faults are considered) and static (i.e., they do not change in the course of computation). We assume that a constant fraction of processors are faulty. We present two fault-tolerant simulation techniques for BSP and CGM: 1.A deterministic simulation that achieves O(1) slowdown for local computations and O((loghp)2) slowdown for communications per superstep, provided that a preprocessing is done that requires O((loghp)2) supersteps and linear (in h) computation per processor in each superstep. 2.A randomized simulation that achieves O(1) slowdown for local computations and O(loghp) slowdown for communications per superstep with high probability, after the same (deterministic) preprocessing as above. Our results are fully scalable over all values of p from Θ(1) to Θ(n). Furthermore, our results imply that if p⩽nε for 0<ε<1 and h=Θ((n/p)δ) for 0<δ⩽1 (which hold in almost all practical BSP and CGM computations), algorithms can be made resilient to a constant fraction of processor faults without any asymptotic slowdown.

Robust Parallel Computations through Randomization

In this paper we present an efficient general simulation strategy for computations designed for fully operational BSP machines of n ideal processors, on n-processor dynamic-fault-prone BSP machines. The fault occurrences are fail- stop and fully dynamic, i.e., they are allowed to happen on-line at any point of the computation, subject to the constraint that the total number of faulty processors may never exceed a known fraction. The computational paradigm can be exploited for robust computations over virtual parallel settings with a volatile underlying infrastructure, such as a NETWORK OF WORKSTATIONS(where workstations may be taken out of the virtual parallel machine by their owner). Our simulation strategy is Las Vegas (i.e., it may never fail, due to backtrack- ing operations to robustly stored instances of the computation, in case of locally unrecoverable situations). It adopts an adaptive balancing scheme of the workload among the currently live processors of the BSP machine. Our strategy is efficient in the sense that, compared with an optimal off-line adversarial computation under the same sequence of fault occurrences, it achieves

Reaching fault diagnosis agreement under a hybrid fault model

The goal of the fault diagnosis agreement (FDA) problem is to make each fault-free processor detect/locate a common set of faulty processors. The problem is examined on processors with mixed fault model (also referred to as hybrid fault model). An evidence-based fault diagnosis protocol is proposed to solve the FDA problem. The proposed protocol first collects the messages which have accumulated in the Byzantine agreement protocol as the evidence. By examining the collected evidence, a fault-free processor can detect/locate which processor is faulty. Then, the network can be reconfigured by removing the detected faulty processors and the links connected to these processors from the network. The proposed protocol can detect/locate the maximum number of faulty processors to solve the FDA problem.

Optimal Adaptive Broadcasting with a Bounded Fraction of Faulty Nodes

We consider broadcasting among n processors, f of which can be faulty. A fault-free processor, called the source, holds a piece of information which has to be transmitted to all other fault-free processors. We assume that the fraction f/n of faulty processors is bounded by a constant γ<1 . Transmissions are fault free. Faults are assumed to be of the crash type: faulty processors do not send or receive messages. We use the whispering model: pairs of processors communicating in one round must form a matching. A fault-free processor sending a message to another processor becomes aware of whether this processor is faulty or fault free and can adapt future transmissions accordingly. The main result of the paper is a broadcasting algorithm working in O( log n) rounds and using O(n) messages of logarithmic size, in the worst case. This is an improvement of the result from [17] where O ((log n) 2 ) rounds were used. Our method also gives the first algorithm for adaptive distributed fault diagnosis in O( log n) rounds.

Optimal fault-tolerant networks with a server

Fast computation through parallel processing and large distributed memory are two important qualities of new multiprocessor computing machines. Various processors of these machines are interconnected through a suitable network. However, a fault in a single processor may drastically reduce the performance rate of these machines. Hence, the designing aspects of fault-tolerant networks have received much attention in recent years. A network N' with n + k processors is called a k-fault-tolerant network with respect to a target network N with n processors If every truncated network of N' with k faulty processors retains the network of N. A processor in a network which is connected to all other processors is called a server. In this paper, we characterize the k-fault-tolerant networks when the target network contains a server.

Optimal fault-tolerant networks with a server

Fast computation through parallel processing and large distributed memory are two important qualities of new multiprocessor computing machines. Various processors of these machines are interconnected through a suitable network. However, a fault in a single processor may drastically reduce the performance rate of these machines. Hence, the designing aspects of fault-tolerant networks have received much attention in recent years. A network N′ with n + k processors is called a k-fault-tolerant network with respect to a target network N with n processors if every truncated network of N′ with k faulty processors retains the network of N. A processor in a network which is connected to all other processors is called a server. In this paper, we characterize the k-fault-tolerant networks when the target network contains a server. © 2000 John Wiley & Sons, Inc.