• Journal of the Korea Computer Industry Society
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• v.7 no.4
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• pp.293-298
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• 2006

A factorization is an extremely important part of multi-level logic synthesis. The number of literals in a factored form is a good estimate of the complexity of a logic function, and can be translated directly into the number of transistors required for implementation. Factored forms are described as either algebraic or Boolean, according to the trade-off between run-time and optimization. A Boolean factored form contains fewer number of literals than an algebraic factored form. In this paper, we present a new method for a Boolean factorization. The key idea is to identify two-cube Boolean subexpression pairs from given expression. Experimental results on various benchmark circuits show the improvements in literal counts over the algebraic factorization based on Bryton's co-kernel cube matrix.

• Journal of the Korea Computer Industry Society
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• v.8 no.4
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• pp.229-236
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• 2007

A factored form is a sum of products of sums of products, ..., of arbitrary depth. Factoring is the process of deriving a parenthesized form with the smallest number of literals from a two-level form of a logic expression. The factored form is not unique and described as either algebraic or Boolean. A Boolean factored form contains fewer number of literals than an algebraic factored form. In this paper, we present a new method for a Boolean factorization. The key idea is to identify two-cube Boolean subexpressions from given two-level logic expression and to extract divisor/quotient pairs. Then, we derive extended divisor/quotient pairs, where their quotients are not cube-free, from the generated divisor/quotients pairs. We generate quotient/quotient pairs from divisor/quotient pairs and extended divisor/quotient pairs. Using the pairs, we make a matrix to generate Boolean factored form based on a technique of rectangle covering.

• Journal of the Korea Society of Computer and Information
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• v.17 no.6
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• pp.83-92
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• 2012

This paper suggests an improved method of grouping minterms based on the Decimal-Valued Matrix (DVM) method. The DVM is a novel approach to Boolean logic minimization method which was recently developed by this author. Using the minterm-based matrix layout, the method captures binary number based minterm differences in decimal number form. As a result, combinable minterms can be visually identified. Furthermore, they can be systematically processed in finding a minimized Boolean expression. Although this new matrix based approach is visual-based, the suggested method in symmetric grouping cell values can become rather messy in some cases. To alleviate this problem, the enhanced DVM method that is based on multi-level groupings of combinable minterms is presented in this paper. Overall, since the method described here provides a concise visualization of minterm groupings, it facilitates a user with more options to explore different combinable minterm groups for a given Boolean logic minimization problem.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.269-278
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• 2000

A Boolean function generates a binary sequence which is frequently used in a stream cipher. There are number of critical concepts which a Boolean function, as a key stream generator in a stream cipher, satisfies. These are nonlinearity, correlation immunity, balancedness, SAC(strictly avalanche criterion), PC(propagation criterion) and so on. In this paper, we present the algorithms for generating random nonlinear combining functions satisfying given correlation immune order and nonlinearity. These constructions can be applied for designing the key stream generators. We use Microsoft Visual C++6.0 for our program.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.615-624
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• 2014

We study special types of matrices. The involutary fuzzy matrices are important in various applications and have many interesting properties. Using the graphical method, we have the zero patterns of involutary fuzzy matrix, that is, involutary Boolean matrices. And we give the construction of all involutary fuzzy matrices for some dimensions and suggest the canonical form of involutary fuzzy matrix.

• Honam Mathematical Journal
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• v.26 no.1
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• pp.3-15
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• 2004

In the fuzzy theory, a matrix A is idempotent if $A^2=A$. The idempotent fuzzy matrices are important in various applications and have many interesting properties. Using the upper diagonal completion process, we have the zero patterns of idempotent fuzzy matrix, that is, the idempotent Boolean matrices. In addition, we give the construction of all idempotent fuzzy matrices for each dimension n.

• Journal of the Korean Mathematical Society
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• v.31 no.3
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• pp.353-365
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• 1994

During the past century, one of the most active and continuing subjects in matrix theory has been the study of those linear operators on matrices that leave certain properties or subsets invariant. Such questions ar usually called "Linear Preserver Problems".

• Journal of the Korean Society for Library and Information Science
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• v.21
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• pp.249-290
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• 1991

Theoretical developments in the information retrieval have offered a number of alternatives to traditional Boolean retrieval. Probability theory and fuzzy set theory have played prominent roles here. Fuzzy set theory is an attempt to generalize traditional set theory by permitting partial membership in a set and this means recognizing different degrees to which a document can match a request. In this study, an experimentation of a document retrieval system using the fuzzy relation matrix of the keywords is described and the results are offered. The queries composed of keywords and Boolean operaters AND, OR, NOT were processed in the retrieval method, and the method was implemented on the PC of 32bit level (30 MHz) in an experimental system. The measurement of the recall ratio and precision ratio verified the effectiveness of the proposed fuzzy relation matrix of keywords and retrieval method. Compared to traditional crisp method in the same document database, the recall ratio increased $10\%$ high although the precision ratio decreased slightly. The problems, in this experiment, to be resolved are first, the design of the automatic data input and fuzzy indexing modules, through which the system . can have the ability of competition and usefulness. Second, devising a systematic procedure for assigning fuzzy weights to keywords in documents and in queries.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.12 no.8
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• pp.3715-3722
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• 2011

This paper presents a new Boolean extraction technique for logic synthesis. This method first calculates divisor/2-cube quotients, 2-cube quotient pairs, and 2-cube quotient matrices. Then we find candidates, which can be common sub-expressions, from 2-cube quotients and matrices. Next, candidate intersection provides the common sub-expressions for several logic expressions. Experimental results show the improvements in literal counts over the previous methods.

• Korean Journal of Computational Design and Engineering
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• v.4 no.1
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• pp.43-51
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• 1999

Producing the relevant information (features) from the CAD models of CAM, called feature recognition or extraction, is the essential stage for the integration of CAD and CAM. Most feature recognition methods, however, have problems in the recognition of intersecting features because they do not handle the intersection geometry properly. In this paper, we propose a machining feature recognition algorithm, which has a solid model consisting of orthogonal primitives as input. The algorithm calculates candidate features and constitutes the Intersection Geometry Matrix which is necessary to represent the spatial relation of candidate features. Finally, it recognizes machining features from the proposed candidate features dividing and growing systems using half space and Boolean operation. The algorithm has the following characteristics: Though the geometry of part is complex due to the intersections of design primitives, it can recognize the necessary machining features. In addition, it creates the Maximal Feature Volumes independent of the machining sequences at the feature recognition stage so that it can easily accommodate the change of decision criteria of machining orders.