• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 1997.11a
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• pp.315-321
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• 1997

본 논문에서는 임의의 부울함수(Boolean function)에 대한 진리표나 출력 시퀀스로부터 논리곱의 배타적 합(exclusive-or sum of products; ESOP)형의 부울함수를 구성하는 알고리듬을 제안한다. 기존에 알려진 카르노맵이나 Quine HcClusky법에 의하여 구해지는 부울함수는 논리곱의 합(sum of product; SOP) 형으로 주어지며 이들 수식은 부정(NOT)논리를 포함하는 경우가 있다. 제안된 알고리듬에 의하여 구해지는 부울함수는 구조적인 등가성을 판별하는데 편리하므로 해쉬함수용 부울함수의 개발에 이용될 수 있다.

• Proceedings of the Korea Association of Information Systems Conference
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• 1997.10b
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• pp.207-213
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• 1997

본 논문은 논리함수의 Module-2 방식에 따라 신경회로망을 구성하고, 구성된 신 경회로망에 의해서 논리함수 XOR을 예를 들어 표현하였다. 논리함수에서 사용된 Module-2 방식은 2치자료를 처리하는 것으로, 논리함수의 대표적인 것이 부울함수(Boole function)이 다. 신경회로망의 입력층에서는 논리함수의 값을 입력하고, 중간층에서는 논리함수의 직교 전개를 이용하고, 출력층에서도 직교전개등을 통하여 최종적인 결과값을 얻는 것이다. 이를 위해서 내적(inner product) 및 norm등을 정의하고, 직교(orthogonal)에 대한 정의를 하였 다. 또한, 부울함수(Boole Function)의 미분에 대한 정의 및 부울함수의 Maclaurin 전개에 대해서도 정의하였다. 본 논문에서 논리함수의 최종적인 출력값은 부울함수의 Maclaurin 전 개에 의해서도 실제적인 값이 출력될 수 있다는 것을 나타내었다.

• 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 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 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.

• 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.

• 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.

• 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.

• 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 Korean Society for information Management
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• v.7 no.1
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• pp.79-95
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• 1990

A retrieval technique was defined as a technique for comparing the document representations. So this study classified retrieval technique in terms of the charactristics of the retrieved set of documents and the representations that are used. The distinction is whether the set of retrieved documents contains only documents whose representations are an exact match with the query, or a partial match with query. For a partial match, the set of retrieved document will include also those that are an exact match with the query. Boolean-logic as one of the exact match retrieval techniques is in current in most of the large operational information retrieval systems despite of its problems and limitatlons. Partial match as an alternative technique has also various problems. Existing information retrieval systems are successful in aSSisting the user whose needs are well- defined (e.g. Boolean-logic), to retrieve relevant documents but it should be successful in providing retrieval assistance to the browser whose information requirements is ill-defined.