Evaluation and Improvements of Boolean Comparison Method Based on Binary Decision Diagrams

An efficient estimation of the ROBDD's complexity

In this paper frequency analysis of spoken Urdu numbers from dasiasifrpsila (zero) to dasianaupsila (nine) is described. Sound samples from multiple speakers were utilized to extract different features. Initial processing of data, i.e. time-slicing and normalizing and was done using a combination of Simulink and MATLAB. Afterwards, the same tools were used for calculation of Fourier descriptions and correlations. The correlation allowed comparison of the same words spoken by the same and different speakers. The analysis presented in this paper is seen as the first step in creating an Urdu speech recognition system. The speech recognition feed-forward neural network models in Matlab were developed. The models and algorithm exhibited high training and testing accuracies. Our major work involves in future use of TI6000 DSK series or linear predictive coding. Such a system can be potentially utilized in implementation of a voice-driven help setup in different systems.

Recognizing spoken Urdu numbers using fourier descriptor and neural networks with Matlab

In particular embodiments, a method includes analyzing a binary decision diagram (BDD) representing a data stream from a sensor to determine a compression rate of the BDD and indicating a sensor malfunction in the sensor if the compression rate of the BDD deviates from a specified compression rate range.

Detecting Sensor Malfunctions Using Compression Analysis of Binary Decision Diagrams

Preprocessing the data is an important step while creating neural network (NN) applications because this step usually has a significant effect on the prediction performance of the model. This paper compares different data processing strategies for NNs for prediction of Boolean function complexity (BFC). We compare NNs' predictive capabilities with (1) no preprocessing (2) scaling the values in different curves based on every curve's own peak and then normalizing to [0,1] range (3) applying z-score to values in all curves and then normalizing to [0,1] range, and (4) logarithmically scaling all curves and then normalizing to [0,1] range. The efficiency of these methods was measured by comparing RMS errors in NN-made BFC predictions for numerous ISCAS benchmark circuits. Logarithmic preprocessing method resulted in the best prediction statistics as compared to other techniques.

Investigating data preprocessing methods for circuit complexity models

This paper analyses and describes the relation between the size of a Boolean function and the number of nodes in its ROBDD representation. Knowing the number of variables and the number of product terms of a Boolean function, we can predict the number of nodes in its reordered binary decision diagram (ROBDD) without building the BDD. A mathematical model for this prediction has been developed. This model can be used to find the maximum number of nodes that can be produced for a given number of variables. The model can also be used to find the number of product terms above which the ROBDD is reduced to 1 node only. We demonstrate that the predictions using this model are quite promising, fast and easy to implement.

http://ieeexplore.ieee.org/iel5/9366/29745/01354387.pdf

Mathematical model to predict the number of nodes in an ROBDD

This paper describes a neural network approach that gives an estimation method for the space complexity of Binary Decision Diagrams (BDDs). A model has been developed to predict the complexity of digital circuits. The formal core of the developed neural network model (NNM) is a unique matrix for the complexity estimation over a set of BDDs derived from Boolean logic expressions with a given number of variables and Sum of Products (SOP) terms. Experimental results show good correlation between the theoretical results and those predicted by the NNM, which will give insights to the complexity of Very Large Scale Integration (VLSI)/Computer Aided Design (CAD) designs. The proposed model is capable of predicting the maximum BDD complexity (MaxBC) and the number of product terms (NPT) in the Boolean function that corresponds to the minimum BDD complexity (MinBC). This model provides an alternative way to predict the complexity of digital VLSI circuits.

/pdf/binary-decision-diagrams-and-neural-networks-bljazdgduu.pdf

Binary Decision Diagrams and neural networks

A large variety of problems in digital system design, combinational optimization and verification can be formulated in terms of operations on Boolean functions Minimizing the average path length (APL) in binary decision diagrams (BDDs) can reduce the evaluation time of Boolean functions represented by these BDDs This paper presents a novel method to generate a BDD with better APL, which reduces the evaluation time, based on a good static variable ordering The method analyses the importance of the given variable order based on the complexity of the sub functions derived from variable substitutions The variable that produces the minimum cumulative complexity for the sub-functions is given priority over other variables Experimental results using benchmark circuits show that the proposed method is an encouraging approach towards minimizing the evaluation time of Boolean functions

Minimum average path length in BDDs based on static variable ordering

A new neural network (NN) approach is proposed in this paper to estimate the Boolean function (BF) complexity. Large number of randomly generated single output BFs has been used and experimental results show good correlation between the theoretical results and those predicted by the NN model. The proposed model is capable of predicting the number of product terms (NPT) in the BF that gives an indication on its complexity.

http://www.wseas.us/e-library/conferences/2006cavtat/papers/523-108.pdf

Boolean function complexity and neural networks

Data transformation is an important step in developing practical and robust neural networks and can take a relatively large percentage of development efforts. In this paper, we present different techniques and their algorithms for data transformation as they apply to the neural network models for predicting Boolean function complexity. The data transformation techniques proposed in this paper yield a high level of model accuracy. The given techniques can also be applied to neural networks developed for other applications.

http://www.wseas.us/e-library/conferences/2007vancouver/papers/558-147.pdf

P.W.C. Prasad

Papers

Mathematical model to predict the number of nodes in an ROBDD

Binary Decision Diagrams and neural networks

Minimum average path length in BDDs based on static variable ordering

Boolean function complexity and neural networks

Data processing for effective modeling of circuit behavior