• Journal of KIISE:Software and Applications
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• v.30 no.7_8
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• pp.642-648
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• 2003

In this paper, we are interested in checking equivalence of FSMs(finite state machines). Two FSMs are equivalent if and only if their responses are always equal with each other with respect to the same external stimuli. Equivalence checking FSMs makes complicated FSM be substituted for simpler one, if they are equivalent. We can also determine the system satisfies the requirements, if they are all written in FSMs. In this paper, we regard equivalence checking problem as model checking one. For doing so, we construct the product model $M ={M_A} {\beta}{M_B} from two FSMs ${M_A} and {M_B}$. And we also get the temporal logic formula ${\Phi}$ from the equivalence checking definition. Then, we can check with model checker whether if satisfies ${\Phi}$, written $M= {.\Phi}$. Two FSMs are equivalent, if $M= {.\Phi}$ Otherwise, it is not equivalent. In that case, model checker generates counterexamples which explain why FSMs are not equivalent. In summary, we solve the equivalence checking problem with model checking techniques. As a result of applying to several examples, we have many satisfiable results.

• Proceedings of the Korean Information Science Society Conference
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• 2003.04c
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• pp.37-39
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• 2003

본 연구에서는 만족성 검사기를 이용하여 두 유한 상태 기계의 행위가 동치인지를 검사한다. 기존의 동치 검사는 대부분 BDD를 기반으로 했었기 때문에 변수 순서 배열 및 내부 BDD노드 폭발 문제에 시달렸었다. 하지만 여기서는 BDD대신 명제 논리를 이용하기 때문에 위와 같은 문제점을 피할 수 있다. 하지만 논리식을 만족성 검사기의 입력 형태인 논리곱 정규형으로 변환하는 과정에서 절의 3기는 식의 크기에 지수적으로 증가하였다.

• Proceedings of the Korean Information Science Society Conference
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• 2002.04b
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• pp.427-429
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• 2002

본 연구에서는 상태도를 평탄화 하는 대신에, 띠러 기계가 동시에 수행하는 병행 기계로 상태도를 표현한 후 ROBDD를 이 용하여 상태도의 동치 여 부를 기호적으로 검사하고자 한다. 상태도가 기능적으로 동치라는 것은, 두 상태도는 같은 함수를 구현하고 있다는 것과 같다. 이 것은 로든 입력 이벤트에 대하여 두 상태도의 반응이 항상동일 한지를 판정함으로써 가능하다. 즉 상태도의 동치 검사는, 입력 이벤트가 같은 상태들의 집합이 모든 입력 에 대 해서 출력 이 같은 상태들인가라는 문제로 축소된다.

• Proceedings of the Korean Information Science Society Conference
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• 2008.06b
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• pp.568-571
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• 2008

하드웨어 개발에 있어서 데이터의 신속한 처리와 공정의 저렴한 비용을 위해 회로의 많은 부분이 게이트 레벨에서 구현된다. 기능 검사는 하드웨어 개발에 있어서 설계의 기능을 분석하는 중요한 설계 흐름이다. 기존의 기능 검사는 사용자의 요구에 의해 하드웨어 시스템이 복잡해지고 개발 주기가 점점 빨라지는 시장의 특성으로 인해 설계자에게 시간적 경제적인 부담감을 준다. 본 연구에서는 설계자에게 가중되는 부담을 극복하고 보다 효율적인 기능 검사를 위해 모델 체킹을 동치성 검사에 적용하는 방법을 제안하고자 한다.

• Proceedings of the Korean Information Science Society Conference
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• 2007.06b
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• pp.354-357
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• 2007

하드웨어 개발에 있어서 데이터의 신속한 처리와 공정의 저렴한 비용을 위해 회로의 많은 부분이 게이트 레벨에서 구현된다. 기능 검사는 하드웨어 개발에 있어서 설계의 기능을 분석하는 중요한 설계 흐름이다. 기존의 기능 검사는 사용자의 요구에 의해 하드웨어 시스템이 복잡해지고 개발 주기가 점점 빨라지는 시장의 특성으로 인해 설계자에게 시간적 경제적인 부담감을 준다. 본 연구에서는 설계자에게 가중되는 부담을 극복하고 보다 효율적인 기능 검사를 위해 모델 체킹을 동치성 검사에 적용하는 방법을 제안하고자 한다.

• Proceedings of the Korean Information Science Society Conference
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• 2003.04a
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• pp.31-33
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• 2003

기능 검사(function simulation)란 하드웨어 시스템의 설계시 모델의 기능, 성능, 표준 준수 여부, 그리고 다른 상위 수준 조건의 관점에서 그 설계를 분석하는 중요한 설계 흐름이다. 하지만 복잡한 기존의 기능 검사의 절차는 사용자의 요구에 의해 하드웨어 시스템이 점점 복잡해지고 정보산업의 발전에 따라 개발 주기가 점점 빨라지는 시장의 특성으로 인해 설계자에게 많은 시간적 경제적인 부담감을 준다. 본 논문에서는 설계자에게 가중되는 부담을 극복하고 보다 효율적인 하드웨어 시스템의 모델링 및 기능 검사를 위해 오토마타 동치성 검사를 통한 하드웨어 시스템의 논리적 정확성 확인 방법론을 제안한다.

• School Mathematics
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• v.15 no.4
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• pp.995-1013
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• 2013

The purpose of this paper was to investigate mathematics teachers' mathematical content knowledge about quadratic curves. Three components of mathematical knowledge are needed for teaching: (i) knowing school mathematics, (ii) knowing process of school mathematics, (iii) making connections between school mathematics and advanced mathematics. 24 mathematics teachers were asked to perform 10 questions based on mathematics curriculum. The results showed that mathematics teachers had some difficulties in conic section definitions and eccentricity definitions of ellipse and hyperbola. And they also got difficulty in Dandellin sphere proof of the equivalence of conic section definitions and quadratic curve definitions. Especially, no one answered correctly to the question about the definition of eccentricity. The ratio of correct answer for the question about constructing tangent lines of quadratic curves is less than that for the question about the applications of the properties of tangent lines. These findings suggests that it is needed that to provide plenty of opportunities to learn mathematical content knowledge in teacher education programs.

• Journal of Elementary Mathematics Education in Korea
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• v.21 no.2
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• pp.309-341
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• 2017

This study aims to investigate an approach to teach percentages in elementary mathematics class by analyzing calculating strategies with percentage the students use to solve the percentage tasks and their percentages of correct answers, as well as types of errors with percentages the students make. For this research 182 sixth graders were examined. The instrument test consists of various task types in reference to the previous study; the percentages tasks are divided into algebraic-geometric, part whole-comparison-change and find part-find whole-find percentage tasks. According to the analysis of this study, percentages of correct answers of students with percentage tasks were lower than we expected, approximately 50%. Comparing the percentages of correct answers according to the task types, the part-whole tasks are higher than the comparison and change tasks, the geometric tasks are approximately equal to the algebraic tasks, and the find percentage tasks are higher than the find whole and find part tasks. As to the strategies that students employed, the percentage of using the formal strategy is not much higher than that of using the informal strategy, even after learning the formal strategy. As an insightful approach for teaching percentages, based on the study results, it is suggested to reinforce the meaning of percentage, include various types of the comparison and change tasks, emphasize the informal strategy explicitly using models prior to the formal strategy, and understand the relations among part, whole and percentage throughly in various percentage situations before calculating.

• Education of Primary School Mathematics
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• v.26 no.3
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• pp.181-197
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• 2023

The importance of reasoning processes based on fractional concepts and number senses, rather than a formalized procedural method using common denominators, has been noted in a number of studies in relation to compare the magnitudes of unlike fractions. In this study, a unlike fraction magnitudes comparison test was conducted on fourth-grade elementary school students who did not learn equivalent fractions and common denominators to analyze the reasoning perspectives of the correct and wrong answers for each of the eight problem types. As a result of the analysis, even students before learning equivalent fractions and reduction to common denominators were able to compare the unlike fractions through reasoning based on fractional sense. The perspective chosen by the most students for the comparison of the magnitudes of unlike fractions is the 'part-whole perspective', which shows that reasoning when comparing the magnitudes of fractions depends heavily on the concept of fractions itself. In addition, it was found that students who lack a conceptual understanding of fractions led to difficulties in having quantitative sense of fraction, making it difficult to compare and infer the magnitudes of unlike fractions. Based on the results of the study, some didactical implications were derived for reasoning guidance based on the concept of fractions and the sense of numbers without reduction to common denominators when comparing the magnitudes of unlike fraction.

• Education of Primary School Mathematics
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• v.27 no.1
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• pp.39-55
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• 2024

Recently, the 2022 revised mathematics curriculum has established achievement standards for equal sign and equality, and efforts have been made to examine teaching methods and student understanding of relational understanding of equal sign. In this context, this study conducted a lesson that emphasized relational understanding in an introduction to equal sign, and compared and analyzed the understanding of equal sign between the experimental group, which participated in the lesson emphasizing relational understanding and the control group, which participated in the standard lesson. For this purpose, two classes of students participated in this study, and the results were analyzed by administering pre- and post-tests on the understanding of equal sign. The results showed that students in the experimental group had significantly higher average scores than students in the control group in all areas of equation-structure, equal sign-definition, and equation-solving. In addition, when comparing the means of students by item, we found that there was a significant difference between the means of the control group and the experimental group in the items dealing with equal sign in the structure of 'a=b' and 'a+b=c+d', and that most of the students in the experimental group correctly answered 'sameness' as the meaning of equal sign, but there were still many responses that interpreted the equal sign as 'answer'. Based on these results, we discussed the implications for instruction that emphasizes relational understanding in equal sign introduction lessons.