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1998 IEEE International Joint Conference on Neural Networks Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36227), 1998

An algorithm is presented to minimize the number of neurons needed for a classifier based on Kohonens Self-Organizing Maps (SOM}, or on any other " code-book type" (or " prototype based" ) classifier such as Kohonens Linear Vector Quantization (LVQ), K-means or nearest neighbor. The neuron minimization problem is formalized as a problem zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA of simplification of Boolean functions, and a geometric interpretation of this simplification is provided. A step by step example with an illustrative classification problem is given.

1996

The author has granted a nonexclusive licence allowing the National Librrily of Canada to reproduce, loan, distribute or sell copies of this thesis in microfonn, paper or electronic formats. The author retains ownership of the copyright in this thesis. Neither the thesis nor substantial extracts fiom it may be printed or othenvise reproduced without the author7 s permission. L'auteur a accordé une licence non exclusive permettant à la Bibliothèque nationale du Canada de reproduire, prêter, distribuer ou vendre des copies de cette thèse sous la forme de microfiche/film, de reproduction sur papier ou sur format électronique. L'auteur conserve la propriété du droit d'auteur qui protège cette thèse. Ni la thèse ni des extraits substantiels de celle-ci ne doivent être imprimés ou autrement reproduits sans son autorisation.

Information and Computation, 1998

In this paper, we address a fundamental problem related to the induction of Boolean logic: Given a set of data, represented as a set of binary "true n-vectors" (or "positive examples") and a set of "false n-vectors" (or "negative examples"), we establish a Boolean function (or an extension) f , so that f is true (resp., false) in every given true (resp., false) vector. We shall further require that such an extension belongs to a certain specified class of functions, e.g., class of positive functions, class of Horn functions and so on. The class of functions represents our a priori knowledge or hypothesis about the extension f , which may be obtained from experience or from the analysis of mechanisms that may or may not cause the phenomena under consideration. The real-world data may contain errors, e.g., measurement and classification errors might come in when obtaining data, or there may be some other influential factors not represented as variables in the vectors. In such situations, we have to give up the goal of establishing an extension that is perfectly consistent with the given data, and we are satisfied with an extension f having the minimum number of misclassifications. Both problems, i.e. the problem of finding an extension within a specified class of Boolean functions, and the problem of finding a minimum error extension in that class, will be extensively studied in this paper. For certain classes we shall provide polynomial algorithms, and for other cases we prove their NP-hardness.

Lecture Notes in Computer Science, 2003

From the very first moment when I knocked his door as a fresh PhD student, to the present day when I am planning my future career, he has never denied me his guidance, support and encouragement. I am greatly privileged to have him as my advisor. I would also like to thank Professor Russ Biagio Altman for serving as my coadvisor and Professor Luca Benini for serving on my dissertation committee. Without the interaction with these two great mentors, my PhD research would have been severely compromised. In addition, I gratefully acknowledge Professor Edward J. McCluskey for supervising my research for the Master's degree and Professor Yoshio Nishi for serving as the chair of my oral defense committee. Special thanks also go to Professor and Mrs. Creger for their continuous encouragement. Additional thanks go to Stanford CAD group members, EPFL LSI people, academic collaborators, and friends. In particular, I would like to thank Eui-Young, Byung-Gon, and Nahmsuk for their invaluable help. I am also greatly indebted to Jerry Yang and Akiko Yamazaki for their vision and generous grant that supported my PhD research. Last but not least, I would like to thank my wife Hyeyoung and my family (especially Hongseop, Young, Byungsoh, Keumgyou, Hanyoung, Hyejin and Yeonsoo) for their never-ending love and support.

Mathematical and Computer Modelling, 1996

critical aspect in the problem of inductive inference is the number of examples needed to accurately infer a Boolean function from positive and negative examples. In this paper, we develop an approach for deriving a sequence of examples for this problem. Some computer experiments indicate that, on the average, examples derived according to the proposed approach lead to the inference of the correct function considerably faster than when examples are derived in a random order.

Journal of Algorithms, 2002

A positive (or monotone) Boolean function is regular if its variables are naturally ordered, left to right, by decreasing strength, so that shifting the nonzero component of any true vector to the left always yields another true vector. This paper considers the problem of recognizing whether a positive function f is regular, where f is given by min T (f) (the set of all minimal true vectors of f). We propose a simple linear time (i.e., O(n|min T (f)|)time) algorithm for it. This improves upon the previous algorithm by Provan and Ball which requires O(n 2 |min T (f)|) time. As a corollary, we also present an O(n(n + |min T (f)|))time algorithm for the recognition problem of 2-monotonic functions.

International Journal of Computer Applications

In this article, a noble approach is presented to classify n-variable Boolean functions in logical way such that each function belonging to a particular class can be traced with respect to a single base function. In the present study, two different methods have been proposed for this classification. The first one is done through the Hamming distance with regards to base 0 (bits of zeros) Boolean function. In the second method, the classification is done to generate all Boolean functions from n variable to n+1 variable through the concatenation methodology. The presented paper also contains two unique and different methodologies for finding the cardinality of different classes. In this classification all the basis Boolean functions were captured into a single class. All the linear and corresponding affine Boolean functions belong to a single class along with other nonlinear Boolean functions except two classes of single cardinality. It has been also observed symmetrical class distrib...

2005

The problem of reconstructing the andor expression of a positive Boolean function starting from a portion of its truth table is solved by adopting a proper algorithm, called Shadow Clustering (SC).

Topics in Intelligent Engineering and Informatics, 2014

Technology transfer: fundamental principles and innovative technical solutions, 2018

The object of research is the method of figurative transformations for Boolean functions minimization. One of the most problematic places to minimize Boolean functions is the complexity of the minimization algorithm and the guarantee of obtaining a minimal function. During the study, the method of equivalent figurative transformations was used, which is based on the laws and axioms of the algebra of logic; minimization protocols for Boolean functions that are used when the truth table of a given function has a complete binary combinatorial system with repetition or an incomplete binary combinatorial system with repetition. A reduction in the complexity of the minimization process for Boolean functions is obtained, new criteria for finding minimal functions are established. This is due to the fact that the proposed method of Boolean functions minimization has a number of peculiarities of solving the problem of finding minimal logical functions, in particular: – mathematical apparatus...