• Proceedings of the Korea Contents Association Conference
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• 2005.11a
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• pp.389-392
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• 2005

Boolean matrices are applied to a variety of areas and used successfully in many applications. There are many researches on the application and multiplication of boolean matrices. Most researches deal with the multiplication of boolean matrices, but all of them focus on the multiplication of just two boolean matrices and very few researches deal with the multiplication of many pairs of two boolean matrices. The paper discusses it is not suitable to use for the multiplication of many pairs of two boolean matrices the algorithm for the multiplication of two boolean matrices that is considered optimal up to now, and suggests a method that can improve the multiplication of a $n{\times}m$ boolean matrix and all $m{\times}k$ boolean matrices.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.1
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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.

• Journal of Information Technology Services
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• v.5 no.1
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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.

• Journal of Information Technology Services
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• v.9 no.4
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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.

• Journal of the Korean Mathematical Society
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• v.44 no.1
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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.

• The Pure and Applied Mathematics
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• v.11 no.1
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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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• v.4 no.1
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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.

• Proceedings of the IEEK Conference
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• 2000.11b
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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.

• Bulletin of the Korean Mathematical Society
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• v.22 no.1
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• pp.63-63
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• 1985

• Proceedings of the IEEK Conference
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• 2005.11a
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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.