• Proceedings of the Korea Contents Association Conference
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• 2018.05a
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• pp.381-382
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• 2018

격자함의 대수와 헤이팅 대수는 부울 대수를 일반화한 논리체계이며 논리적 함의(${\rightarrow}$)를 이항연사자로 갖는 대수적 체계를 갖는다. 본 논문에서는 격자함의 대수와 헤이팅 대수가 서로 다른 대수체계를 갖는다는 것을 예로 보이고, 이들의 차이점을 조사한다. 또한 격자함의 대수, 헤이팅 대수, 그리고 부울 대수의 관계를 알아본다.

• Journal of Advanced Navigation Technology
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• v.15 no.5
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• pp.781-788
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• 2011

A sphere-packing problem is to find an arrangement of the spheres to fill as large area of the given space as possible, and covering problems are optimization problems which are dual problems to the packing problems. We generalize the concepts of the weight and the Hamming distance for a binary code to those of Boolean algebra. In this paper, we define a weight and a distance on a Boolean algebra and research some properties of the weight and the distance. Also, we prove the notions of the sphere-packing bound and the Gilbert-Varshamov bound on Boolean algebra.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.8 no.3
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• pp.39-48
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• 1998

GAC(GloabvalAvalanche Characteristics)은 부울함수가 전파특성 관점에서 얼마나 우수한지를 전체적인 관점에서 나타내는 특성으로 Zhang-Zheng(1995)에 의해서 제안되었다. GAC을 측정하는 기준으로는 와 가 있으며, 두 기준값이 작을수록 부울함수는 보다 우수한 전파특성을 갖는다. Zhang-Zheng은 GAC이 우수한 균형인 부울함수를 설계하는 두 가지 방법을 제시하였으며, 균형인 부울함수f의 대수적 차수가 3 이상일 때 의 하한이 $2^이라고 추측하였다. 본 논문에서는Zhang-Zheng의 방법보다 우수한 새로운 설계방법을 제시하며, 이를 이용하여 그들의 추측에 대한 반례를 제시한다.한다.

• Journal of the Korean Institute of Telematics and Electronics
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• v.13 no.6
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• pp.20-23
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• 1976

A boolean algebra method for computing the reliability in a communication network is prosented. Given the set of all simple paths between two nodes in a network, the terminal reliability can be symbolically computed by the Boolean operation which is named parallel operation. The method seems to be promising for both oriented and nonoriented network.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.11 no.11
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• pp.4597-4603
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• 2010

A factorization is a very important part of multi-level logic synthesis. The number of literals in a factored form is an 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 nonkernel Boolean pairs from given expression. Experimental results on various benchmark circuits show the improvements in literal counts over previous other factorization methods.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.10 no.11
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• pp.3227-3233
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• 2009

A method for performing Boolean resubstitution is proposed. This method is efficiently implemented using division matrix. It begins by creating an algebraic division matrix from given two logic expressions. By introducing Boolean properties and adding literals into the algebraic division matrix, we make the Boolean division matrix. Using this extended division matrix, Boolean substituted expressions are found. Experimental results show the improvements in the literal counts over well-known logic synthesis tools for some benchmark circuits.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.14 no.4
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• pp.49-59
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• 2004

Boolean function synthesize problem is to find a boolean expression with in/outputs of original function. This problem can be modeled into a 0-1 integer programming. In this paper, we find a boolean expressions of S-boxes of DES for an example, whose algebraic structure has been unknown for many years. The results of this paper can be used for efficient hardware implementation of a function and cryptanalysis using algebraic structure of a block cipher.

• 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.

• Proceedings of the Korea Information Processing Society Conference
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• 2008.11a
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• pp.722-725
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• 2008

복합질환(complex disease)의 원인과 작용 모델을 찾기 위해 여러 가지 통계적인 방법들과 기계 학습(machine learning)의 방법 등이 사용되고 있다. 소수 SNP의 작용모델을 찾는 방법은 많이 알려져 있지만 다수 SNP의 작용 모델을 효과적으로 찾는 방법은 거의 연구되어 있지 않다. 본 연구에서는 원인 SNP들의 작용을 부울 식(boolean expression)으로 나타내고, 유전 알고리즘(genetic algorithm)을 이용하여 예측 정확도가 높은 부울 식을 구성하였으며 실제 자료와 생성된 자료에 대하여 제안한 모델의 성능을 측정하였다.

• Korean Journal of Logic
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• v.12 no.1
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• pp.1-24
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• 2009

이 논문에서 우리는 집합의 두 점 사이의 관계를 소개하고, '가깝다'와 '충분히 가깝다'의 위상적인 개념을 다양하게 정의할 수 있음을 보인다. 또한 직관주의 논리와 관계가 있는 De Morgan frame을 소개하고 pre-order에 의하여 정의된 동치관계로 만들어진 동치류들의 집합을 기저로 생성된 위상 공간이 extremally disconnected 임을 보인다.