On t-diagnosability of multicore systems with symmetric circulant structure

We consider system level diagnostics for multicore (modular) computational systems with multiple faults. Test results for faulty units correspond to the well-known model of Preparata, Metze, and Chien (PMC-model). We prove conditions for t-diagnosability without repair for systems whose structure is a symmetric circulant graph. We present the rules of comparative analysis for test results for units in the considered multicore system that ensure a correct and complete testing of its technical state for a number of faulty units that does not exceed a certain predefined threshold.     

Efficient Algorithms for Anonymous Byzantine Agreement

This paper considers the Byzantine agreement problem in a completely connected network of anonymous processors. In this network model the processors have no identifiers and can only detect the link through which a message is delivered. We present a polynomial-time agreement algorithm that requires 3⌊(n−t)t/(n−2t)⌋+4 rounds, where n>3t is the number of processors and t is the maximal number of faulty processors that the algorithm can tolerate. We also present an early-stopping variant of the algorithm.     

Analysis of the possibility of local diagnosis in computer systems with circulant structure based on redundancy in the number of analyzed testing results

Local diagnosis at multiple faults when a faultless/faulty state for each module is identified only by the results of comparative analysis of testing results of the modules that have physical connections with diagnosable module is considered. Conditions at which the state can be defined not for all modules (dead state) are studied. Features of the dead state for separate modules and for the system on the whole, the use of which allows reducing the labor intensiveness of the analysis of local diagnosability of a system, are obtained. In the paper, the possibility of redundancy in the number of dead states at using the redundancy in the number of testing results participating in comparative analysis is shown for systems with circulant diagnostic structure. It is proved that for systems with optimal circulant diagnostic structure such redundancy makes a sufficient condition for excluding dead states.     

Near-optimal message routing and broadcasting in faulty hypercubes

A distributed routing algorithm for faulty hypercubes is described. This algorithm uses a directed depth-first approach to find a path between the sender and receiver of a message whenever at least one non-faulty path exists. We show that, when an arbitrary number of elements of the hypercube can be faulty, the algorithm always routes messages using fewer than 2N hops, whereN is the number of nodes in the hypercube. This performance is shown to be within a factor of two of the optimal worst-case routing efficiency. Through foult simulations, we show that, even when up to half of the elements in the cube are faulty, complete the analysis, we prove that our algorithm is deadlock-free. Finally, we present two extensions of the algorithm. The first uses local storage to reduce the overhead of the algorithm while the second allows reliable broadcasting in the presence of an arbitrary number of faults.Supported in part by the National Science Foundation under Grant CCR-9010547.Supported in part by the National Science Foundation Instrumentation Grant CDA-8820627.     

Autonomous fault-diagnosis and decision-making algorithm for determining faulty nodes in distributed wireless networks

In this paper, we address fault-diagnosis agreement (FDA) problems in distributed wireless networks (DWNs) with arbitrary fallible nodes and healthy access points. We propose a new algorithm to reach an agreement among fault-free members about the faulty ones. The algorithm is designed for fully connected DWN and can also be easily adapted to partially connected networks. Our contribution is to reduce the bit complexity of the Byzantine agreement process by detecting the same list of faulty units in all fault-free members. Therefore, the malicious units can be removed from other consensus processes. Also, each healthy unit detects a local list of malicious units, which results in lower packet transmissions in the network. Our proposed algorithm solves FDA problems in 2t+1 rounds of packet transmissions, and the bit complexity in each wireless node is O(n^t+1).     

Group testing problem with two defectives

We consider the classical (2,N) group testing problem, i.e., the problem of finding two defectives among N elements. We propose a new adaptive algorithm such that for $N = \left\lfloor {2\tfrac{{t + 1}} {2} - t \cdot 2\tfrac{t} {4}} \right\rfloor $ the problem can be solved in t tests.     

基于互连网络系统故障的新型自适应诊断算法

互连网络的故障诊断是网络系统可靠性分析的重要内容。PMC模型是一种重要的网络故障模型。针对具有哈密顿环的互连网络(也称哈密顿网络),利用分治回环思想,提出了一种新的基于PMC故障模型自适应的诊断算法。其核心思想是,首先对哈密顿网络进行序列划分,然后对得到的每个01序列的结节进行回环诊断,最后利用回环诊断的结果对非01序列的节点进行诊断。对于一个具有多个01序列的互连网络,该算法通过有限次轮回的测试,能准确的定位系统中的故障节点,对于正确节点的诊断可靠度能无限接近100%。当系统中存在的回测边越多,该算法的诊断效果越好。     

Local diagnostication in computer systems with the circulant structure

Studies are made of the possibility of diagnostication at the system level. The objects of the investigation are multiprocess fail-safe systems with the circulant diagnostic structure, in which the t-multiple failures at the level of processing modules are accepted. The results (outcomes) of the testing correspond to the known model of Preparata, Metze, and Chien. Conditions are found at which the technical state of each processing module can be defined on the basis of the analysis of the results of its testing only from adjacent modules.     

Perspective silhouette of a general swept volume

We present an efficient and robust algorithm for computing the perspective silhouette of the boundary of a general swept volume. We also construct the topology of connected components of the silhouette. At each instant t, a three-dimensional object moving along a trajectory touches the envelope surface of its swept volume along a characteristic curve K^t. The same instance of the moving object has a silhouette curve L^t on its own boundary. The intersection K^t∩L^t contributes to the silhouette of the general swept volume. We reformulate this problem as a system of two polynomial equations in three variables. The connected components of the resulting silhouette curves are constructed by detecting the instances where the two curves K^t and L^t intersect each other tangentially on the surface of the moving object. We also consider a general case where the eye position changes while moving along a predefined path. The problem is reformulated as a system of two polynomial equations in four variables, where the zero-set is a two-manifold. By analyzing the topology of the zero-set, we achieve an efficient algorithm for generating a continuous animation of perspective silhouettes of a general swept volume.     

A novel strategy of pareto-optimal solution searching in multi-objective particle swarm optimization (MOPSO)

In multi-objective particle swarm optimization (MOPSO) algorithms, finding the global optimal particle (gBest) for each particle of the swarm from a set of non-dominated solutions is very difficult yet an important problem for attaining convergence and diversity of solutions. First, a new Pareto-optimal solution searching algorithm for finding the gBest in MOPSO is introduced in this paper, which can compromise global and local searching based on the process of evolution. The algorithm is implemented and is compared with another algorithm which uses the Sigma method for finding gBest on a set of well-designed test functions. Finally, the multi-objective optimal regulation of cascade reservoirs is successfully solved by the proposed algorithm.     

On input-output linearization of discrete-time nonlinear systems

We consider a nonlinear discrete-time system of the form Σ: x(t+1)=f(x(t), u(t)), y(t) =h(x(t)), where x ε R^N, u ε R^m, y ε R^q and f and h are analytic. Necessary and sufficient conditions for local input-output linearizability are given. We show that these conditions are also sufficient for a formal solution to the global input-output linearization problem. Finally, we show that zeros at infinity of ε can be obtained by the structure algorithm for locally input-output linearizable systems.     

On Approximate Jumbled Pattern Matching in Strings

Given a string s, the Parikh vector of s, denoted p(s), counts the multiplicity of each character in s. Searching for a match of a Parikh vector q in the text s requires finding a substring t of s with p(t)=q. This can be viewed as the task of finding a jumbled (permuted) version of a query pattern, hence the term Jumbled Pattern Matching. We present several algorithms for the approximate version of the problem: Given a string s and two Parikh vectors u,v (the query bounds), find all maximal occurrences in s of some Parikh vector q such that u≤q≤v. This definition encompasses several natural versions of approximate Parikh vector search. We present an algorithm solving this problem in sub-linear expected time using a wavelet tree of s, which can be computed in time O(n) in a preprocessing phase. We then discuss a Scrabble-like variation of the problem, in which a weight function on the letters of s is given and one has to find all occurrences in s of a substring t with maximum weight having Parikh vector p(t)≤v. For the case of a binary alphabet, we present an algorithm which solves the decision version of the Approximate Jumbled Pattern Matching problem in constant time, by indexing the string in subquadratic time.     

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.     

Reasoning about faulty quantum programs

We show how to use a programming language for formally describing and reasoning about errors in quantum computation. The formalisation is based on the concept of performing the correct operation with probability at least p, and the erroneous one with probability at most 1 − p. We apply the concept to two examples: Bell’s inequalities and the Deutsch–Jozsa quantum algorithm. The former is a fundamental thought experiment aimed at showing that Quantum Mechanics is not “local and realist”, and it is used in quantum cryptography protocols. We study it assuming faulty measurements, and we derive hardware reliability conditions that must be satisfied in order for the experiment to support its conclusions. The latter is a quantum algorithm for efficiently solving a classification problem for Boolean functions. The algorithm solves the problem with no error, but when we introduce faulty operations it becomes a two-sided error algorithm. Reasoning is accomplished via standard programming laws and quantum laws.     

One-to-one communication in twisted cubes under restricted connectivity

The dimensions of twisted cubes are only limited to odd integers. In this paper, we first extend the dimensions of twisted cubes to all positive integers. Then, we introduce the concept of the restricted faulty set into twisted cubes. We further prove that under the condition that each node of the n-dimensional twisted cube TQ _n has at least one fault-free neighbor, its restricted connectivity is 2n − 2, which is almost twice as that of TQ _n under the condition of arbitrary faulty nodes, the same as that of the n-dimensional hypercube. Moreover, we provide an O(NlogN) fault-free unicast algorithm and simulations result of the expected length of the fault-free path obtained by our algorithm, where N denotes the node number of TQ _n . Finally, we propose a polynomial algorithm to check whether the faulty node set satisfies the condition that each node of the n-dimensional twisted cube TQ _n has at least one fault-free neighbor.     

A fast pessimistic diagnosis algorithm for generalized hypercube multicomputer systems

The reliability of processors is an important issue for designing a massively parallel processing system for which fault-tolerant computing is crucial. In order to achieve high system reliability and availability, a faulty processor (node) when found should be replaced by a fault-free processor. Within a multiprocessor system, the technique of identifying faulty nodes by constructing tests on the nodes and interpreting the test outcomes is known as system-level diagnosis. The topological structure of a multicomputer system can be modeled by a graph of which the vertices and edges correspond to nodes and links of the system, respectively. This work presents a system-level diagnosis algorithm for a generalized hypercube which is an attractive variance of a hypercube. The proposed algorithm is based on the PMC model and can isolate all faulty nodes to within a set which contains at most one fault-free node. If the total number of nodes to be diagnosed in a generalized hypercube is N, the proposed algorithm can run in O(Nlog?N) time, and being superior to Yang??s algorithm proposed in 2004, it can diagnose not only a hypercube but also a generalized hypercube.     

Syndrome-decoding algorithms for static-diagnosis models

The problem of finding fault patterns consistent with a given syndrome is discussed for graph-theoretical diagnosis models such as the fault-diagnosis and self-diagnosis models. The fault-diagnosis model consists of two types of vertices, fault units and measurements, and is expressed by a bipartite graph. Faulty states of a fault unit always imply abnormal states of all the measurements which are adjacent to the unit, otherwise a measurement remains normal. A self-diagnosis model consists of one type of unit which has the capability of testing other units and being tested itself. The testing relation is represented by a directed arc; this produces test outcomes which are invalid if the testing unit is faulty. The inverse system which yields a fault pattern from a corresponding syndrome for fault-diagnosis models is studied and a syndrome-decoding algorithm is proposed which works for some class of diagnosis models with observation noise. The algorithm uses a similar measure to the syndrome-decoding algorithm of error-correcting codes which use the Hamming distance. Another measure is presented for the self-diagnosis model expressed by a directed graph and this measure is characterized by a ranking method.     

An Online Diagnosable Fault-Tolerant Redundancy System

This paper presents an online diagnosable fault-tolerant system: N-unit t-fault tolerablesystem. The number of units N in the system can be either odd or even. The relationshipbetween N and t (the number of faulty units which can be tolerated) is presented. The approachof an optimum N- unit t-fault tolerable system is also given. As an example, a 4-unit 2-faulttolerable system is discussed. The reliability and mean time to failure of 4-unit 2-fault tolerablesystem are shown to be higher than 5MR (5-modular redundancy) and TMR (Triple ModulerRedundancy) system reliabilities. The amount of hardware components in a 4-unit t-faulttolerable system is simpler than 5MR. The complexity of switching circuit for N-unit t-faulttolerable system increases only linearly with respect of the number of modules. Our scheme isalso simpler than the hybrid redundancy system. Some theorems for the online diagnosis of N-unit t-fault systems are given and proved.     

On the route-oriented method of system diagnostics in digital systems structured as a symmetric bipartite graph

We propose a method for organizing the route-oriented method for diagnostics of digital systems (DS) with the structure of a symmetric bipartite graph. To describe the results of testing individual units, we use the Preparata-Metze-Chien model (PMC). We suppose that the system has a diagnostic monitor that initiates the diagnostic processes. To estimate the value of diagnosability in the analyzed DS, we use the method of potential syndromes. We show that the analyzed DS are no more than 1-diagnosable without repair. For a system including seven processors and seven memory units, we consider an example with an unreliable diagnostics of three faulty components.     

Covering arrays avoiding forbidden edges

Covering arrays (CAs) can be used to detect the existence of faulty pairwise interactions between parameters or components in a software system. The generalization considered here applies to the situation in which some input combinations are invalid, a requirement quite common in software testing. In this paper, we study covering arrays avoiding forbidden edges (CAFEs), where certain pairwise interactions are forbidden while all others must be covered, and we aim to minimize the number of tests. We establish a theoretical framework for this problem, by providing connections to the edge clique covering problem, lower and upper bounds, complexity results and a recursive construction. We also give an algorithm for the case of binary alphabets.