Fast and simple algorithm of a parity checker for a large residue numbers is presented. A new set of RNS moduli with 2r-(2l1) form for fast modular multiplication is proposed. The proposed RNS moduli has a large dynamic range for a large RNS number. The parity of a residue number can be checked by the Chinese remainder theorem (CRT). A CRT-based parity checker is simply organized by the Montgomery reduction method (MRM), implemented by using multipliers and the carry-save adder array. We present a fast parity checker with minimal hardware processed in three clock cycles for 32-bit RNS modulus set.

This paper is concerned with fuzzy modeling in some reduction methods of inference rules with gradient descent. Reduction methods are presented, which have a reduction mechanism of the rule unit that is applicable in three parameters--the central value and the width of the membership function in the antecedent part, and the real number in the consequent part--which constitute the standard fuzzy system. In the present techniques, the necessary number of rules is set beforehand and the rules are sequentially deleted to the prespecified number. These methods indicate that techniques other than the reduction approach introduced previously exist. Experimental results are presented in order to show that the effectiveness differs between the proposed techniques according to the average inference error and the number of learning iterations.

Reduction of the complexity of the NLMS algorithm has recceived attention in the area of adaptive filtering. A processing cost reduction method, in which the component of the weight vector is updated when the absolute value of the sample is greater than or equal to an arbitrary threshold level, has been proposed. The convergence analysis of the processing cost reduction method with white Gaussian data has been derived. However, a convergence analysis of this method with correlated Gaussian data, which is important for an actual application, is not studied. In this paper, we derive the convergence cheracteristics of the processing cost reduction method with correlated Gaussian data. From the analytical results, it is shown that the range of the gain constant to insure convergence is independent of the correlation of input samples. Also, it is shown that the misadjustment is independent of the correlation of input samples. Moreover, it is shown that the convergence rate is a function of the threshold level and the eigenvalues of the covariance matrix of input samples as well as the gain constant.

Reduction of the complexity of the NLMS algorithm has received attention in the area of adaptive filtering. A processing cost reduction method, in which the component of the weight vector is updated when the absolute value of the sample is greater than or equal to the average of the absolute values of the input samples, has been proposed. The convergence analysis of the processing cost reduction method has been derived from a low-pass filter expression. However, in this analysis the effect of the weignt vector components whose adaptations are skipped is not considered in terms of the direction of the gradient estimation vector. In this paper, we use an arbitrary value instead of the average of the absolute values of the input samples as a threshold level, and we derive the convergence characteristics of the processing cost reduction method with arbitrary threshold level for zero-mean white Gaussian samples. From the analytical results, it is shown that the range of the gain constant to insure convergence and the misadjustment are independent of the threshold level. Moreover, it is shown that the convergence rate is a function of the threshold level as well as the gain constant. When the gain constant is small, the processing cost is reduced by using a large threshold level without a large degradation of the convergence rate.

We propose a new type of Graph Rewriting Systems (GRS) that provide a theoretical foundation for using the reduction method which plays an important role on analyze network reliability. By introducing this GRS, several facts were obtained as follows: (1) We clarified the reduction methods of network reliability analysis in the theoretical framework of GRS. (2) In the framework of GRS, we clarified the significance of the completeness in the reduction methods. (3) A procedure of recognizing complete systems from only given rewriting rules was shown. Specially the procedure (3) is given by introducing a boundary graph (B-Graph). Finally an application of GRS to network reliability analysis is shown.