• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.847-865
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• 2017

For a finite or an infinite set X, let $2^X$ be the power set of X. A class of simple graph, called strong Boolean graph, is defined on the vertex set $2^X{\setminus}\{X,{\emptyset}\}$, with M adjacent to N if $M{\cap}N={\emptyset}$. In this paper, we characterize the annihilating-ideal graphs $\mathbb{AG}(R)$ that are blow-ups of strong Boolean graphs, complemented graphs and preatomic graphs respectively. In particular, for a commutative ring R such that AG(R) has a maximum clique S with $3{\leq}{\mid}V(S){\mid}{\leq}{\infty}$, we prove that $\mathbb{AG}(R)$ is a blow-up of a strong Boolean graph if and only if it is a complemented graph, if and only if R is a reduced ring. If assume further that R is decomposable, then we prove that $\mathbb{AG}(R)$ is a blow-up of a strong Boolean graph if and only if it is a blow-up of a pre-atomic graph. We also study the clique number and chromatic number of the graph $\mathbb{AG}(R)$.

• 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 Korean Society for information Management
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• v.12 no.1
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• pp.87-97
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• 1995

Boolean retrieval systems have been most widely used in the area of information retrieval due to easy implementation and efficient retrieval. Conventional Boolean retrieval systems. however, cannot rank retrieved documents in decreasing order of query-document similarities because they cannot compute similarity coefficients between queries and documents. Extended Boolean models such as fuzzy set. Waller-Kraft, Paice, P-Norm and Infinite-One have been developed to provide the document ranking facility. In extended Boolean models, the formulas evaluating Boolean operators AND and OR are an important component to affect the quality of document ranking. In this paper we present mathematical properties of the formulas, and analyse their effect on retrieval effectiveness. Our analyses show that P-Norm is the most suitable for achieving high retrieval effectiveness.

• Journal of Mechanical Science and Technology
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• v.19 no.2
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• pp.549-557
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• 2005

The requirements of multi-resolution models of feature-based solids, which represent an object at many levels of feature detail, are increasing for engineering purposes, such as analysis, network-based collaborative design, virtual prototyping and manufacturing. To provide multi-resolution models for various applications, it is essential to generate adequate solid models at varying levels of detail (LOD) after feature rearrangement, based on the LOD criteria. However, the non-commutative property of the union and subtraction Boolean operations is a severe obstacle to arbitrary feature rearrangement. To solve this problem we propose history-based Boolean operations that satisfy the commutative law between union and subtraction operations by considering the history of the Boolean operations. Because these operations guarantee the same resulting shape as the original and reasonable shapes at the intermediate LODs for an arbitrary rearrangement of its features, various LOD criteria can be applied for multi-resolution modeling in different applications.

• The KIPS Transactions:PartD
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• v.15D no.6
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• pp.777-784
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• 2008

Recently in the field of model checking, to overcome the state explosion problem, the method of using a SAT-solver is mainly researched. To use a SAT-solver, the system to be verified is translated into CNF and the Boolean cardinality constraint is widely used in translating the system into CNF. In BCC it is dealt with set of boolean variables, but there is no translating method of the sequence among Boolean variables. In this paper, we propose methods for translating the problem, which is extracting a subsequence with length k from a sequence of Boolean variables, into CNF formulas. Through experimental results, we show that our method is more efficient than using only BCC.

• 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 Institute of Information Security & Cryptology
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• v.26 no.1
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• pp.5-15
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• 2016

Power analysis attacks are techniques to analyze power signals to find out the secrets when cryptographic algorithm is performed. One of the most famous countermeasure against power analysis attacks is masking methods. Masking types are largely classified into two types which are boolean masking and arithmetic masking. For the cryptographic algorithm to be used with boolean and arithmetic masking at the same time, the converting algorithm can switch between boolean and arithmetic masking. In this paper we propose an algorithm for switching from boolean to arithmetic masking using storage size at less cost than ones. The proposed algorithm is configured to convert using the look-up table without the least significant bit(LSB), because of equal the bit of boolean and arithmetic masking. This makes it possible to design a converting algorithm compared to the previous algorithm at a lower cost without sacrificing performance. In addition, by applying the technique at the LEA it showed up to 26 percent performance improvement over existing techniques.

• Journal of the Korean Institute of Telematics and Electronics
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• v.13 no.3
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• pp.1-6
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• 1976

In this paper, a method of test pattern generation for the functional failure in both combinational and sequentlal logic networks by using exterded Boole an difference is proposed. The proposed technique provides a systematic approach for the test pattern generation procedure by computing Boolean difference of the Boolean function that represents the Logic network for which the test patterns are to be generated. The computer experimental results show that the proposed method is suitable for both combinational and asynchronous sequential logic networks. Suitable models of clocked flip flops may make it possible for one to extend this method to synchronous sequential logic networks.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.5 no.1
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• pp.3-16
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• 1995

In this paper, we deal with the cryptographic properties of Boolean functions generated by recursively extended methods from the points of balancedness, nonlinearity and correlation properties. First, we propose a new concept 'Strict Uncorrelated Criterion(SUC)' for two Boolean functions as a necessary condition for constructing Boolean functions of S-box which can be guaranteed to be resistant against Differential cryptanalysis, then we show that the recurively extended Boolean functions with particular form preserve the SUC. We also examine the correlation properties of Boolean functions using Walsh-Hadamard transformations and apply them to discuss nonlinearity, correlation properties and SUC of semi-bent function which is defined over odd dimensional vector space. Finally, we compare semi-bent function with Boolean functions which are generated by other similar recursive methods.

• Journal of KIISE:Software and Applications
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• v.26 no.10
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• pp.1219-1229
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• 1999

일반적으로 AND, OR, NOT과 같은 연산자를 사용하는 불리언 질의는 사용자의 검색의도를 정확하게 표현할 수 있기 때문에 검색 전문가들은 불리언 질의를 사용하여 높은 검색성능을 얻는다고 알려져 있지만, 일반 사용자는 자신이 원하는 정보를 불리언 형태로 표현하는데 익숙하지 않다. 본 논문에서는 검색성능의 향상과 사용자 편의성을 동시에 만족하기 위하여 사용자의 자연어 질의를 확장 불리언 질의로 자동 변환하는 방법론을 제안한다. 먼저 자연어 질의를 범주문법에 기반한 구문분석을 수행하여 구문트리를 생성하고 연산자 및 키워드 정보를 추출하여 구문트리를 간략화한다. 다음으로 간략화된 구문트리로부터 명사구를 합성하고 키워드들에 대한 가중치를 부여한 후 불리언 질의를 생성하여 검색을 수행한다. 또한 구문분석의 오류로 인한 검색성능 저하를 최소화하기 위하여 상위 N개 구문트리에 대해 각각 불리언 질의를 생성하여 검색하는 N-BEST average 방법을 제안하였다. 정보검색 실험용 데이타 모음인 KTSET2.0으로 실험한 결과 제안된 방법은 수동으로 추출한 불리언 질의보다 8% 더 우수한 성능을 보였고, 기존의 벡터공간 모델에 기반한 자연어질의 시스템에 비해 23% 성능향상을 보였다. Abstract There have been a considerable evidence that trained users can achieve a good search effectiveness through a boolean query because a structural boolean query containing operators such as AND, OR, and NOT can make a more accurate representation of user's information need. However, it is not easy for ordinary users to construct a boolean query using appropriate boolean operators. In this paper, we propose a boolean query formulation method that automatically transforms a user's natural language query into a extended boolean query for both effectiveness and user convenience. First, a user's natural language query is syntactically analyzed using KCCG(Korean Combinatory Categorial Grammar) parser and resulting syntactic trees are structurally simplified using a tree-simplifying mechanism in order to catch the logical relationships between keywords. Next, in a simplified tree, plausible noun phrases are identified and added into the same tree as new additional keywords. Finally, a simplified syntactic tree is automatically converted into a boolean query using some mapping rules and linguistic heuristics. We also propose an N-BEST average method that uses top N syntactic trees to compensate for bad effects of single incorrect top syntactic tree. In experiments using KTSET2.0, we showed that a proposed method outperformed a traditional vector space model by 23%, and surprisingly manually constructed boolean queries by 8%.