• 한국콘텐츠학회:학술대회논문집
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• 한국콘텐츠학회 2005년도 추계 종합학술대회 논문집
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• pp.389-392
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• 2005

불리언 행렬은 다양한 분야에 응용되어 유용하게 사용되고 있으며, 불리언 행렬의 응용과 곱셈에 대하여 많은 연구가 수행되었다. 대부분의 연구에서는 불리언 행렬의 곱셈을 다루고 있으나 모두 두 불리언 행렬 곱셈에 관심을 두고 있으며 많은 불리언 행렬 쌍의 곱셈은 극히 소수의 연구에서 보이고 있다. 본 논문에서는 기존에 제시된 두 불리언 행렬의 최적 곱셈 알고리즘이 많은 불리언 행렬 쌍에 대한 곱셈을 해야 하는 경우 부적합함을 보이고 하나의 $n{\times}m$ 불리언 행렬과 모든 $m{\times}k$ 불리언 행렬의 곱셈을 개선시킬 수 있는 방법을 제시한다.

• 전기학회논문지
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• 제66권1호
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• pp.137-143
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• 2017

In this paper, we investigate static control of Boolean networks described in the framework of semi-tensor product (STP) operation. The control objective is to determine control input nodes and their logical values so as to stabilize the considered Boolean network to a desired fixed point or cycle. Using topology of Boolean networks such as incidence matrix and hub nodes, a set of appropriate control input nodes is selected, and based on STP operations, we assign constant control inputs so that the controlled network can converge to a prescribed fixed point or cycle. To validate applicability of the proposed scheme, we conduct a numerical study on the problem of determining control input nodes for a Boolean network representing hierarchical differentiation of myeloid progenitors.

• 한국IT서비스학회지
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• 제5권1호
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• pp.191-198
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• 2006

Boolean matrices have been successfully used in various areas, and many researches have been performed on them. However, almost all the researches focus on the efficient multiplication of two boolean matrices and no research has been shown to deal with the multiplication of all boolean matrices and their consecutive multiplications. The paper suggests a mathematical theory that enables the efficient consecutive multiplications of all $l{\times}n,\;n{\times}m,\;and\;m{\times}k$ boolean matrices, and discusses its computational complexity and the execution results of the consecutive multiplication algorithm based on the theory.

• 한국IT서비스학회지
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• 제9권4호
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• pp.219-229
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• 2010

The Green's equivalence relations have played a fundamental role in the development of semigroup theory. They are concerned with mutual divisibility of various kinds, and all of them reduce to the universal equivalence in a group. Boolean matrices have been successfully used in various areas, and many researches have been performed on them. Studying Green's relations on a monoid of boolean matrices will reveal important characteristics about boolean matrices, which may be useful in diverse applications. Although there are known algorithms that can compute Green relations, most of them are concerned with finding one equivalence class in a specific Green's relation and only a few algorithms have been appeared quite recently to deal with the problem of finding the whole D or J equivalence relations on the monoid of all $n{\times}n$ Boolean matrices. However, their results are far from satisfaction since their computational complexity is exponential-their computation requires multiplication of three Boolean matrices for each of all possible triples of $n{\times}n$ Boolean matrices and the size of the monoid of all $n{\times}n$ Boolean matrices grows exponentially as n increases. As an effort to reduce the execution time, this paper shows an isomorphism between the R relation and L relation on the monoid of all $n{\times}n$ Boolean matrices in terms of transposition. introduces theorems based on it discusses an improved algorithm for the J relation computation whose design reflects those theorems and gives its execution results.

• 대한수학회지
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• 제44권1호
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• pp.169-178
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• 2007

We consider the set of $n{\times}n$ idempotent matrices and we characterize the linear operators that preserve idempotent matrices over Boolean algebras. We also obtain characterizations of linear operators that preserve idempotent matrices over a chain semiring, the nonnegative integers and the nonnegative reals.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제11권1호
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• pp.1-14
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• 2004

Due to the development of computer network and mobile communications, the security in image data and other related source are very important as in saving or transferring the commercial documents, medical data, and every private picture. Nonetheless, the conventional encryption algorithms are usually focusing on the word message. These methods are too complicated or complex in the respect of image data because they have much more amounts of information to represent. In this sense, we proposed an efficient secret symmetric stream type encryption algorithm which is based on Boolean matrix operation and the characteristic of image data.

• Journal of applied mathematics & informatics
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• 제4권1호
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• pp.147-166
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• 1997

The convergence of the power sequence of an $n{\times}n$ fuzzy matrix has been studied. Some theoretical necessary and sufficient con-ditions have been established for the power sequence to be convergent generally. Furthermore as one of our main concerns the convergence index was studied in detail especially for some special types of Boolean matrices. Also it has been established that the convergence index is bounded by $(n-1)^2+1$ from above for an arbitrary $n{\times}n$ fuzzy matrix if its power sequence converges. Our method is concentrated on the limit behavior of the power se-quence. It helped us to make our proofs be simpler and more direct that those in pure algebraic methods.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2000년도 추계종합학술대회 논문집(2)
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• pp.337-340
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• 2000

In this paper, we put forth a procedure that target low power logic synthesis based on XOR representation of Boolean functions, and the results of synthesis procedure are a multi-level XOR form with minimum switching activity. Specialty, this paper show a method to extract the common cubes or kernels by Boolean matrix and rectangle covering, and to estimate the power consumption in terms of the extracted common sub-functions.

• 대한수학회보
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• 제22권1호
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• pp.63-63
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• 1985

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2005년도 추계종합학술대회
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• pp.849-852
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• 2005

A factorization is an extremely important part of multi-level logic synthesis. The number of literals in a factored from 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 Brayton's co-kernel cube matrix.