Earticle

바둑은 적어도 2,500년 이상의 역사를 지녔고 그동안 인간 고유의 게임 영역으로 여겨왔으나, 2016년 컴퓨터 바둑인 알파고에 의해 제압된 마지막 보드게임이 되었다. 바둑에서의 사활문제는 컴퓨터 바둑을 구축 시 반 드시 해결해야 되는 기본 문제 영역이 된다. 연역적 추론은 이미 알고 있는 판단을 근거로 새로운 사실을 추 론하는 논리학의 용어이다. 본 논문에서는 연역적 추론을 위해 제약 충족 방법을 활용하여 사활문제와 직결 되는 3궁, 4궁, 5궁, 6궁의 원형 안형을 표현하는 4-튜플의 형식을 찾고자 했다. 이후 생성된 4-튜플의 형식 을 갖고 점 패턴 매칭을 활용하여 각 궁도의 원형 안형의 갯수를 파악하고자 했다. 실험 결과에 따른 4-튜플 형식의 갯수는 3궁 1개, 4궁 3개, 5궁 4개, 6궁 8개가 있음을 알 수 있었다. 또한 각 궁도의 원형 안형의 갯 수는 3궁 2개, 4궁 5개, 5궁 12개, 6궁 35개가 존재함을 찾아냈다. 마지막으로 컴퓨터 바둑에서의 사활문제 해결을 위해 원형 안형들을 4-튜플 형식의 변형인 5-튜플 형식으로도 제시하였다.

Go has a history of at least 2,500 years and has been regarded as a unique game field for humans, but in 2016 it became the last board game to be overpowered by alphaGo, a computer Go. The life-and-death problem in Go becomes a fundamental problem domain that must be solved when implementing a computer Go. Deductive reasoning is a term in logic that infers new facts based on known judgements. In this paper, we tried to find the 4-tuple forms representing the prototypical eye shapes of 3-eyes, 4-eyes, 5-eyes, and 6-eyes, which are directly related to the life-and-death problems, by using the constraint satisfaction method for deductive reasoning. Afterwards, we tried to figure out the number of prototypical eye shapes of each eyes by using point pattern matching with the generated 4-tuple form. According to the experimental results, we can see that the 4-tuple forms have 1 for 3-eyes, 3 for 4-eyes, 4 for 5-eyes, and 8 for 6-eyes. We also found that the numbers of prototypical eye shapes for each eyes are 2 for 3-eyes, 5 for 4-eyes, 12 for 5-eyes, and 35 for 6-eyes. Lastly, for solving the life-and-death problem in computer Go, we also presented prototypical eye shapes as the 5-tuple forms which are variants of 4-tuple forms.

This paper presents only a matching algorithm based on Delaunay triangulation and Parametrization from the extracted minutiae points. This method maps local neighborhood of points of two different point sets to unit-circle using topology information by Delaunay triangulation method from feature points of real fingerprint. Then, a linked convex polygon that includes an interior point is constructed as one-ring which is mapped to unit-circle using Parametrization that keep shape preserve. In local matching, each area of polygon in unit-circle is compared. If the difference of two areas are within tolerance, two polygons are consider to be matched and then translation, rotation and scaling factors for global matching are calculated.

바둑은 2,500년 이상의 역사를 지녔고, 바둑에서의 사활문제는 컴퓨터 바둑을 구축 시에 반드시 해결해야 되는 기본 문제영역이 된다. 본 논문에서는 사활문제와 직결되는 3, 4, 5, 6궁에 대한 원형 안형의 개수 확인과 4-튜플 형식으로 표현된 원형 안형을 분류하고자 했다. 실험은 몬테카를로 방법과 점 패턴 매칭에 의해 수행되었다. 실험 결과에 따르면 원형 안형의 개수는 3궁 2개, 4궁 5개, 5궁 12개, 6궁 35개가 된다. 아울러 4-튜플 형식으로 된 원형 안형을 분류하면 3궁 1가지, 4궁 3가지, 5궁 4가지, 6궁 8가지로 분류된다.

Go has a history of more than 2,500 years, and the life-and-death problems in Go is a fundamental problem domain that must be solved when implementing a computer Go. We attempted to determine the numbers of prototypical eye shapes with 3, 4, 5, and 6 eyes that are directly related to the life-and-death problems, and to classify the prototypical eye shapes represented in 4-tuple forms. Experiment was conducted by Monte-Carlo method and point pattern matching. According to the experimental results, the numbers of prototypical eye shapes were 2 for 3-eye, 5 for 4-eye, 12 for 5-eye, and 35 for 6-eye shapes. Further, using a 4-tuple form, we classified prototypical eye shapes into 1 for 3-eye, 3 for 4-eye, 4 for 5-eye, and 8 for 6-eye shapes.