Since the characteristic of current information systems is the dynamic change of their configurations and scales with non-stop provision of their services, the system management should inevitably rely on autonomic computing. Since fault tolerance is one of the important system management issues, it should also be incorporated in an autonomic computing environment. This paper argues what should be taken into consideration and what approach could be available to realize the fault tolerance in such environments.

First, the incorporation of the alternative ways of representing the solution to the traveling salesman problem by neural network is proposed to deal with the asymmetric tolerance of neural networks to unidirectional faults. Next, in order to cope with the simultaneous occurrence of a s-a-0 and s-a-1 faults, the triplication scheme with a proper merging function is considered. Finally, the combination of the alternative representations and the triplication scheme is used.

Usually, parameters in software reliability growth models are not known, and they must be estimated by using observed failure data. Several estimation methods have been proposed, but most of them have restrictions such as the existence of derivatives on evaluation functions. On the other hand, genetic algorithms (GA) provide us with robust optimization methods in many fields. We apply GA to the parameter estimation of the hyper-geometric distribution software reliability growth model. Experimental result shows that GA is effective in the parameter estimation and removes restrictions from software reliability growth models.

The hyper-geometric distribution model (HGDM) has been proposed for estimating the number of faults initially resident in a program at the beginning of the test/debug process. However, the parameters of the hyper-geometric distribution necessary for making the estimation were previously determined by the 3-dimensional exhaustive search and therefore, much time was needed to get the numerical result. The authors demonstrate, using real test/debug data of programs, that the least square sum method can be well applied to the estimation of such parameters of the hyper-geometric distribution model. Thus, the time needed for calculating the estimates can be reduced greatly.>

Six ways to estimate parameters of the hypergeometric distribution are investigated, and their accuracies are examined comparatively. It is demonstrated that the least-squares sum method is the best one among those tried, and can be applied to real test/debug data for estimating the number of faults still resident in a program after test/debugging. By this method the estimation time can be reduced greatly.>

The hyper-geometric distribution is used to estimate the number of initial faults residual in software at the beginning of the test-and-debug phase. The hyper-geometric distribution growth model (HGD model) is well suited to making estimates for the observed growth curves of the accumulated number of detected faults. The advantage of the proposed model is the applicability to all kinds of observed data. By application of a single model, exponential growth curves as well as S-shaped growth curves can be estimated. The precise formulation of the HGD model is presented. The exact relationship of this model to the NHPP Goel-Okumoto growth model and the delayed S-shaped growth model is shown. With the introduction of a variable fault detection rate, the goodness of fit of the estimated growth curve to the growth curve of real observed faults is increased significantly. Different examples of the applicability of the model to real observed data are presented.>

Models used to estimate the number of residual software faults are examined. The models were developed by universities and industries in Japan. It has been shown that the hypergeometric distribution model can be applied to real data of different types. The relationship between the model based on the hypergeometric distribution and those based on the nonhomogeneous Poisson process has been revealed.>

It is shown that the hyper-geometric distribution model can be applied to different types of test-and-debug data to estimate the number of initial software faults. Examples show that the fitness of the estimated growth curves of the model to real data is satisfactory. The relationship of the model to those proposed earlier is clarified. Some of them can be expressed as a special case of the proposed model. The S-shaped characteristic of the growth curve can also be introduced using this model.>

Models based on the hyper-geometric distribution for estimating the number of residual software faults are proposed. The application of the basic model shows that its fit to real data is good. Two ways of improving the model, using a segmentation technique and composite estimation, respectively, are shown. The segmentation technique appears quite effective, particularly when the growth curve of the cumulative number of detected faults bends sharply. The applications of these models to real data are demonstrated.>

A universal single transition time (STT) state assignment is a way to give a valid STT state assignment in which all state variables that must change in a given transition are allowed to change simultaneously without critical races for any asynchronous sequential machine regardless of the configuration of its flow table. This paper presents a new systematic procedure for constructing universal STT state assignments and shows that the procedure can give better upper bounds on the number of state variables required for realizing asynchronous normal flow tables than any known universal STT state assignments, although there is some difference in standpoint between earlier works and the present one. It is further shown that the procedure can also be applied to improve the best known bounds for (2, 1) separating systems which are known to be less restricted universal assignments. The feature of the procedure lies in the idea that two binary code vectors are assigned to each internal state. In the resulting universal STT assignments, the number of state variables required is given by 2 · m1.59 where m = [log2 n], n being the number of states and [X] being the least integer ≥ X. Furthermore, the resulting (2, 1) separating systems require 2 ·m state variables.

One of two constructive procedures for universal single transition time (STT) state assignments presented in the paper [1] by Friedman et al. is not correct. A correct constructive procedure can be obtained by simply modifying the procedure of the literature with an additional restriction.

The problem of the realization of fail-safe asynchronous sequential circuits was recently studied by Patterson and Sawin. This correspondence presents a different approach to the same subject which, in some cases, yield us simpler realization than those by the methods ever proposed, combining the notion of the ordered partition with Tracey's method for the state assignment of asynchronous sequential circuit.

A method for the realization of fail-safe sequential circuits is presented where flip-flops are employed for representing the internal states. First, such a design technique where the circuit will be trapped in an erroneous state into which it is transferred by a fault is shown. Further, the condition for assuring that the circuit will be dropped into the particular (predetermined) final state when a fault exists is described. Finally, some extensions of the technique are attempted.

A sequential machine must have certain redundant information in order to be capable of correcting error. As past inputs and past states are redundant, a sequential machine with error correction capability is constructable by making use of these elements of past information. This paper describes conditions of state assignments, numbers of required redundant state variables, and estimation of reliability of failure-tolerant sequential machines.

A fail-safe sequential machine is one that produces safe-side output when failures occur in the machine. This paper presents a new method of realization of fail-safe sequential machines under the following assumptions: 1) failure is caused by a single fault of element in the machine, 2) output of faulty element is stuck at one or zero, and 3) input does not malfunction.

A method of decomposing logical functions using three input majority gates is given. This method requires that at least one of the inputs to the gate be specified, and from this the other inputs may be found. For unate functions one of the variables may be completely separated at each level. A method using a Karnaugh map is proposed for finding the best function to use as the specified input, which will make the other inputs to the majority gate easier to synthesize.