• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.507-521
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• 2019

For any $m{\times}n$ nonbinary Boolean matrix A, its spanning column rank is the minimum number of the columns of A that spans its column space. We have a characterization of spanning column rank-1 nonbinary Boolean matrices. We investigate the linear operators that preserve the spanning column ranks of matrices over the nonbinary Boolean algebra. That is, for a linear operator T on $m{\times}n$ nonbinary Boolean matrices, it preserves all spanning column ranks if and only if there exist an invertible nonbinary Boolean matrix P of order m and a permutation matrix Q of order n such that T(A) = PAQ for all $m{\times}n$ nonbinary Boolean matrix A. We also obtain other characterizations of the (spanning) column rank preserver.

• Journal of the Korean Institute of Telematics and Electronics
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• v.18 no.1
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• pp.25-34
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• 1981

Any logical stuckft faults in multivalued combinational circuits are analyzed using the concept of Boolean difference. The algebra employed is the implementation oriented algebra developed by Allen and Givone. All the lines in the circuit are classified into five types according to their properties. For each type, the equation that represents the complete test set is derived and proved. All the results in examples are confumed to be correct by comparing the truth tables of the normal and faulty circuits.

• Journal of the Korean Mathematical Society
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• v.36 no.6
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• pp.1181-1190
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• 1999

Zero-term rank of a matrix is the minimum number of lines (rows or columns) needed to cover all the zero entries of the given matrix. We characterized the linear operators that preserve zero-term rank of the m×n matrices over binary Boolean algebra.

• Honam Mathematical Journal
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• v.37 no.3
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• pp.287-297
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• 2015

In this paper, we investigate $T_1$ Boolean subalgebras of the Boolean algebra consisting all regular closed sets in a space and their Wallman covers. In particular, we will give sufficient and necessary conditions of spaces X satisfying ${\beta}E_{cc}(X)=E_{cc}({\beta}X)$.

• Communications of the Korean Mathematical Society
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• v.19 no.2
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• pp.197-204
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• 2004

Every orthomodular lattice satisfying the loop lemma is the direct product of a Boolean algebra and an irreducible path-connected orthomodular lattice.

• The Mathematical Education
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• v.17 no.1
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• pp.29-34
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• 1978

• Kyungpook Mathematical Journal
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• v.43 no.4
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• pp.539-545
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• 2003

We present a set of equations that axiomatizes the class of all lattice implication algebras. The construction is different from the one given in [7], and the proof is direct: i.e., it does not rely on results from outside the realm of the lattice implication algebras, such as the theory of BCK-algebras. Then we show that the lattice H implication algebras are nothing more than the familiar Boolean algebras. Finally we obtain some negative results for the embedding of lattice implication algebras into Boolean algebras.

• Journal of Korea Society of Industrial Information Systems
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• v.16 no.5
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• pp.9-19
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• 2011

In many instances a concise form of logic is often required for building today's complex systems. The method described in this paper can be used for a wide range of industrial applications that requires Boolean type of logic minimization. Unlike some of the previous logic minimization methods, the proposed method can be used to better gain insights into the logic minimization process. Based on the decimal valued matrix, the method described here can be used to find an exact minimized solution for a given Boolean function. It is a visual based method that primarily relies on grouping the cell values within the matrix. At the same time, the method is systematic to the extent that it can also be computerized. Constructing the matrix to visualize a logic minimization problem should be relatively easy for the most part, particularly if the computer-generated graphs are accompanied.

• The Journal of Korean Association of Computer Education
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• v.15 no.1
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• pp.65-72
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• 2012

Generally, a logic function has many factored forms. The problem of finding more compact factored form is one of the basic operations in logic synthesis. In this paper, we present a new method for factoring Boolean functions to assist in educational logic designs. Our method for factorization is to implement two-cube Boolean division with supports of an expression. The number of literals in a factored form is a good estimate of the complexity of a logic function. Our empirical evaluation shows the improvements in literal counts over previous other factorization methods.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.721-729
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• 2007

In this paper, we have characterizations of idempotent matrices over general Boolean algebras and chain semirings. As a consequence, we obtain that a fuzzy matrix $A=[a_{i,j}]$ is idempotent if and only if all $a_{i,j}$-patterns of A are idempotent matrices over the binary Boolean algebra $\mathbb{B}_1={0,1}$. Furthermore, it turns out that a binary Boolean matrix is idempotent if and only if it can be represented as a sum of line parts and rectangle parts of the matrix.