An on-line algorithm for the location of cross point faults in programmable logic arrays

An on-line algorithm is developed for the location of single cross point faults in a PLA (FPLA). The main feature of the algorithm is the determination of a fault set corresponding to the response obtained for a failed test. For the apparently small number of faults in this set, all other tests are generated and a fault table is formed. Subsequently, an adaptive procedure is used to diagnose the fault. Functional equivalence test is carried out to determine the actual fault class if the adaptive testing results in a set of faults with identical tests. The large amount of computation time and storage required in the determination, a priori, of all the fault equivalence classes or in the construction of a fault dictionary are not needed here. A brief study of functional equivalence among the cross point faults is also made.

A fuzzy dynamic flood routing model for natural channels

A fuzzy dynamic flood routing model (FDFRM) for natural channels is presented, wherein the flood wave can be approximated to a monoclinal wave. This study is based on modification of an earlier published work by the same authors, where the nature of the wave was of gravity type. Momentum equation of the dynamic wave model is replaced by a fuzzy rule based model, while retaining the continuity equation in its complete form. Hence, the FDFRM gets rid of the assumptions associated with the momentum equation. Also, it overcomes the necessity of calculating friction slope (S-f) in flood routing and hence the associated uncertainties are eliminated. The fuzzy rule based model is developed on an equation for wave velocity, which is obtained in terms of discontinuities in the gradient of flow parameters. The channel reach is divided into a number of approximately uniform sub-reaches. Training set required for development of the fuzzy rule based model for each sub-reach is obtained from discharge-area relationship at its mean section. For highly heterogeneous sub-reaches, optimized fuzzy rule based models are obtained by means of a neuro-fuzzy algorithm. For demonstration, the FDFRM is applied to flood routing problems in a fictitious channel with single uniform reach, in a fictitious channel with two uniform sub-reaches and also in a natural channel with a number of approximately uniform sub-reaches. It is observed that in cases of the fictitious channels, the FDFRM outputs match well with those of an implicit numerical model (INM), which solves the dynamic wave equations using an implicit numerical scheme. For the natural channel, the FDFRM Outputs are comparable to those of the HEC-RAS model.

An On-Line Algorithm for the Location of Cross Point Faults in Programmable Logic Arrays

An on-line algorithm is developed for the location of single cross point faults in a PLA (FPLA). The main feature of the valgorithm is the determination of a fault set corresponding to the response obtained for a failed test. For the apparently small number of faults in this set, all other tests are generated and a fault table is formed. Subsequently, an adaptive procedure is used to diagnose the fault. Functional equivalence test is carried out to determine the actual fault class if the adaptive testing results in a set of faults with identical tests. The large amount of computation time and storage required in the determination, a priori, of all the fault equivalence classes or in the construction of a fault dictionary are not needed here. A brief study of functional equivalence among the cross point faults is also made.

Estimation of fuzzy memberships from histograms

Based on the conclusions drawn in the bijective transformation between possibility and probability, a method is proposed to estimate the fuzzy membership function for pattern recognition purposes. A rational function approximation to the probability density function is obtained from the histogram of a finite (and sometimes very small) number of samples. This function is normalized such that the highest ordinate is one. The parameters representing the rational function are used for classifying the pattern samples based on a max-min decision rule. The method is illustrated with examples.

Foldable compatibility matrix for the folding of programmable logic arrays

This paper describes a switching theoretic algorithm for the folding of programmable logic arrays (PLA). The algorithm is valid for both column and row folding, although it has been presented considering only the simple column folding. The pairwise compatibility relations among all the pairs of the columns of the PLA are mapped into a square matrix, called the compatibility matrix of the PLA. A foldable compatibility matrix (FCM), a new concept introduced by the author, is then derived from the compatibility matrix. A new theorem called the folding theorem is then proved. The theorem states that the existence of an m by 2m FCM is both necessary and sufficient to fold 2m columns of the n column PLA (2m ≤ n). Once an FCM is obtained, the ordered pairs of foldable columns and the re-ordering of the rows are readily determined.

Static RAM cell for ternary logic

A novel CMOS static RAM cell for ternary logic systems is described. This cell is based on the lambda diode. The operation of the cell has been simulated using the SPICE 2G program. The results of the simulation are given.

A Note on Easily Testable Realizations for Logic Functions

It is shown that at most, n + 3 tests are required to detect any single stuck-at fault in an AND gate or a single faulty EXCLUSIVE OR (EOR) gate in a Reed-Muller canonical form realization of a switching function.

Reed-Muller Canonical Forms in Multivalued Logic

Canonical forms for m-valued functions referred to as m-Reed-Muller canonical (m-RMC) forms that are a generalization of RMC forms of two-valued functions are proposed. m-RMC forms are based on the operations ?m (addition mod m) and .m (multiplication mod m) and do not, as in the cases of the generalizations proposed in the literature, require an m-valued function for m not a power of a prime, to be expressed by a canonical form for M-valued functions, where M > m is a power of a prime. Methods of obtaining the m-RMC forms from the truth vector or the sum of products representation of an m-valued function are discussed. Using a generalization of the Boolean difference to m-valued logic, series expansions for m-valued functions are derived.

An imprecise fuzzy risk approach for water quality management of a river system

Uncertainty plays an important role in water quality management problems. The major sources of uncertainty in a water quality management problem are the random nature of hydrologic variables and imprecision (fuzziness) associated with goals of the dischargers and pollution control agencies (PCA). Many Waste Load Allocation (WLA)problems are solved by considering these two sources of uncertainty. Apart from randomness and fuzziness, missing data in the time series of a hydrologic variable may result in additional uncertainty due to partial ignorance. These uncertainties render the input parameters as imprecise parameters in water quality decision making. In this paper an Imprecise Fuzzy Waste Load Allocation Model (IFWLAM) is developed for water quality management of a river system subject to uncertainty arising from partial ignorance. In a WLA problem, both randomness and imprecision can be addressed simultaneously by fuzzy risk of low water quality. A methodology is developed for the computation of imprecise fuzzy risk of low water quality, when the parameters are characterized by uncertainty due to partial ignorance. A Monte-Carlo simulation is performed to evaluate the imprecise fuzzy risk of low water quality by considering the input variables as imprecise. Fuzzy multiobjective optimization is used to formulate the multiobjective model. The model developed is based on a fuzzy multiobjective optimization problem with max-min as the operator. This usually does not result in a unique solution but gives multiple solutions. Two optimization models are developed to capture all the decision alternatives or multiple solutions. The objective of the two optimization models is to obtain a range of fractional removal levels for the dischargers, such that the resultant fuzzy risk will be within acceptable limits. Specification of a range for fractional removal levels enhances flexibility in decision making. The methodology is demonstrated with a case study of the Tunga-Bhadra river system in India.

Fuzzy waste load allocation model: a multiobjective approach

Fuzzy Waste Load Allocation Model (FWLAM), developed in an earlier study, derives the optimal fractional levels, for the base flow conditions, considering the goals of the Pollution Control Agency (PCA) and dischargers. The Modified Fuzzy Waste Load Allocation Model (MFWLAM) developed subsequently is a stochastic model and considers the moments (mean, variance and skewness) of water quality indicators, incorporating uncertainty due to randomness of input variables along with uncertainty due to imprecision. The risk of low water quality is reduced significantly by using this modified model, but inclusion of new constraints leads to a low value of acceptability level, A, interpreted as the maximized minimum satisfaction in the system. To improve this value, a new model, which is a combination Of FWLAM and MFWLAM, is presented, allowing for some violations in the constraints of MFWLAM. This combined model is a multiobjective optimization model having the objectives, maximization of acceptability level and minimization of violation of constraints. Fuzzy multiobjective programming, goal programming and fuzzy goal programming are used to find the solutions. For the optimization model, Probabilistic Global Search Lausanne (PGSL) is used as a nonlinear optimization tool. The methodology is applied to a case study of the Tunga-Bhadra river system in south India. The model results in a compromised solution of a higher value of acceptability level as compared to MFWLAM, with a satisfactory value of risk. Thus the goal of risk minimization is achieved with a comparatively better value of acceptability level.

Assessment of SET Logic Robustness Through Noise Margin Modeling

A compact model for noise margin (NM) of single-electron transistor (SET) logic is developed, which is a function of device capacitances and background charge (zeta). Noise margin is, then, used as a metric to evaluate the robustness of SET logic against background charge, temperature, and variation of SET gate and tunnel junction capacitances (CG and CT). It is shown that choosing alpha=CT/CG=1/3 maximizes the NM. An estimate of the maximum tolerable zeta is shown to be equal to plusmn0.03 e. Finally, the effect of mismatch in device parameters on the NM is studied through exhaustive simulations, which indicates that a isin [0.3, 0.4] provides maximum robustness. It is also observed that mismatch can have a significant impact on static power dissipation.

Classification of Indian meteorological stations using cluster and fuzzy cluster analysis, and Kohonen artificial neural networks

The present study deals with the application of cluster analysis, Fuzzy Cluster Analysis (FCA) and Kohonen Artificial Neural Networks (KANN) methods for classification of 159 meteorological stations in India into meteorologically homogeneous groups. Eight parameters, namely latitude, longitude, elevation, average temperature, humidity, wind speed, sunshine hours and solar radiation, are considered as the classification criteria for grouping. The optimal number of groups is determined as 14 based on the Davies-Bouldin index approach. It is observed that the FCA approach performed better than the other two methodologies for the present study.

Modeling and Analysis of Noise Margin in SET Logic

In this paper the static noise margin for SET (single electron transistor) logic is defined and compact models for the noise margin are developed by making use of the MIB (Mahapatra-Ionescu-Banerjee) model. The variation of the noise margin with temperature and background charge is also studied. A chain of SET inverters is simulated to validate the definition of various logic levels (like VIH, VOH, etc.) and noise margin. Finally the noise immunity of SET logic is compared with current CMOS logic.

Two-way converter logic for positive and negative binary numbers

This paper describes a hardware implementation of a two-way converter logic by which conversion between numbers from positive to negative binary representation is possible. Index terms: (i) Negative radix, (ii) Positive radix, (iii) Two-way conversion.