• Proceedings of the Korean Information Science Society Conference
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• 2003.04a
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• pp.881-883
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• 2003

하드웨어 검증과 모델 체킹 등의 분야에서, SAT(satisfiability problem)나 항진 명제 검사(tautology checking)는 매우 중요한 문제이다. 그러나 이들은 모두 NP-complete 문제이므로 그 복잡도가 매우 크다. 이를 해결하기 위해 여러 가지 연구가 이루어져 왔으며, 여러 효율적인 알고리즘이 존재한다. 이러한 알고리즘은 대부분 일반 표현식을 CNF(conjunctive normal form)로 바꾸어 입력 형식으로 사용한다. 이 논문에서는 일반 표현식을 입력으로 받아 DNF로 변환한 뒤 DNF의 특성을 이용하여 SAT를 검사하는 효율적인 방법을 제시한다.

• Proceedings of the Korean Information Science Society Conference
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• 2003.10a
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• pp.517-519
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• 2003

하드웨어 검증과 모델 체킹 등의 분야에서, SAT(satisfiability problem)나 항진 명제 검사(tautology checking)는 매우 중요한 문제이다. 그러나 이들은 모두 NP-complete 문제이므로 그 복잡도가 매우 크다. 이를 해결하기 위한 여러 연구가 진행되고 있고, 그 결과 성능이 좋은 solver들이 개발되었다. 하지만 문제가 커질수록 solver의 처리 시간이 급격하게 증가한다. 이 논문에서는 solver가 복잡한 문제를 더 효율적으로 풀기 위해 논문“Local search for Boolean relations on the basis of unit propagation”［5］에서 제안된 preprocessor(전처리기), P_EQ의 개념을 설명하고, 실험을 통한 결과를 제시한다.

• Journal of the Korea Society of Computer and Information
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• v.6 no.2
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• pp.129-142
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• 2001

This paper reviews real option theory and its recent application to management studies involving highly risky business. Three problems are identified in previous studies that created confusions in the application of real option view. It is proposed in this paper that by explicitly stating the underlying real asset on which real option is written, researchers can prevent real option analysis from becoming a tautology and clarify three problems identified in this paper.

• Korean Journal of Logic
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• v.23 no.2
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• pp.117-159
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• 2020

In the early Wittgenstein's Tractatus, both philosophy of logic and that of mathematics belong to the most crucial subjects of it. What is the philosophical view of the early Wittgenstein in the Tractatus? Did he, for example, accept Frege and Russell's logicism or reject it? How did he stipulate the relation between logic and mathematics? How should we, for example, interpretate "Mathematics is a method of logic."(6.234) and "The Logic of the world which the proposition of logic show in the tautologies, mathematics shows in equations."(6.22)? Furthermore, How did he grasp the relation between mathematical equations and tautologies? In this paper, I will endeavor to answer these questions.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.10 no.10
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• pp.1773-1778
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• 2006

This paper propose the method of constructing the Digital Logic Systems based on the Improved Automatic Theorem Proving Techniques(IATP) over Finite Fields. The proposed method is as following. First, we discuss the background and the important mathematical properties for Finite Fields. Also, we discuss the concepts of the Automatic Theorem Proving Techniques(ATP) including the syntactic method and semantic method, and discuss the basic properties for the Alf. In this step, we define several definitions of the IAIP, Table Pseudo Function Tab and Equal. Next, we propose the T-gate as Building Block(BB) and describe the mathematical representation for the notation of T-gate. Then we discuss the important properties for the T-gate. Also, we propose the several relationships that are Identity relationship, Constant relationship, Tautology relationship and Mod R cyclic relationship. Then we propose Mod R negation gate and the manipulation of the don't care conditions. Finally, we propose the algorithm for the constructing the method of the digital logic systems over finite fields. The proposed method is more efficiency and regularity than my other earlier methods. Thet we prospect the future research and prospects.

• Journal of KIISE:Software and Applications
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• v.28 no.9
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• pp.662-668
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• 2001

Since the problem of disproving a tautology is as hard as the problem of proving it, no polynomial time algorithm for falsification(or testing invalidity) is feasible. Previous algorithms are mostly based on either divide-and-conquer or graph representation. Most of them demonstrated satisfactory results on a variety of input under certain constraints. However, they have experienced difficulties dealing with big input. We propose a new falsification algorithm using a Merge Rule to produce a counterexample by constructing a minterm which is not satisfied by an input expression in DNF(Disjunctive Normal Form). We also show that the algorithm is consistent and sound. The algorithm is based on a greedy method which would seek to maximize the number or terms falsified by the assignment made at each step of the falsification process. Empirical results show practical performance on big input to falsify randomized nontautological problem instances, consuming O(nm$^2$) time, where n is the number of variables and m is number of terms.