論理関数のグラフ表現の性質と双対比への応用

逻辑函数的图形表示的性质及其对偶对比的应用

• 批准号: 09780267
• 负责人: 武永 康彦
• 金额: $ 1.09万
• 依托单位: The University of Electro-Communications
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Encouragement of Young Scientists (A)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-09780267/
• 关键词: 論理関数; 二分決定木; 素項; 二分決定グラフ; しきい値関数; 双対比; tree-shellable関数; 双対化

本研究では、二分決定木や分岐プログラムなど理論上実際上重要な、グラフによる論理関数の表現法について、研究を行なってきた。本年度の研究成果の詳細は以下の通りである。1. 分岐プログラムの性質と表現能力に関する研究分岐プログラムの一種で、効率的な論理関数の表現法として知られる二分決定グラフについて、論理関数の正の例および負の例からの学習可能性について研究を行なった。具体的には、すべての例を満たす最小サイズの二分決定グラフを求める問題が、関数をしきい値関数に制限した場合でもNP困難であることを示した。2. 論理関数双対化等への応用前年度に提案した、論理関数を二分木表現の1つの経路が1つの素項に対応するような正論理関数のクラスについて、決定木の変数順序を固定した場合(ordered tree-shellable関数)、固定しない場合(tree-shellable関数)にわけて、さらに研究を進めた。(Ordered)tree-shellableであることがわかれば、効率良い双対化等、その特長の活用が可能だが、それにはこれらのクラスに属するかどうかの判定が必要となる。Quadratic関数(積和形表現の各積項のリテラル数が2個)に対しては多項式時間で判定可能であるが、一般の場合についても、リテラル数が2個の積項だけを取り出した関数が(ordered)tree-shellableであることが、必要条件となることを示した。また、前年度のプログラムを改良し、変数の置換によって等価となる関数を1個とみなした場合も含め、6変数までの関数に対して、これらの性質を持つ関数の個数を具体的に求めた。

This study is divided into two parts: the first part is important in theory, the second part is important in theory, the third part is important in theory, the fourth part is important in theory, and the fourth part is important in theory. This year's research results are detailed below. 1. A study on the relationship between the nature and performance of the diversity group and the study on the possibility of learning the diversity group by determining the positive and negative examples of the logical relationship between the diversity group and the performance of the logical relationship. Specific examples of this problem include the following: 2. The logical correlation pairs are proposed in the previous year, and the logical correlation pairs are divided into two parts. The first part of the logical correlation pairs is divided into two parts. The second part of the logical correlation pairs is divided into two parts. The first part of the logical correlation pairs is divided into three parts. The second part of the logical correlation pairs is divided into two parts. The first part of the logical correlation pairs is divided into three parts. The second part of the logical correlation pairs is divided into two parts. The third part of the logical correlation pairs is divided into three parts. The fourth part of the logical correlation pairs is divided into two parts. The fourth part of the logical correlation pairs is divided into three parts. The fourth part of the logical correlation pairs is divided into two parts. The fourth part of the logical correlation pairs is divided into three parts. The fourth part of the logical correlation pairs is divided into two parts. The fourth part of the logical correlation pairs is divided into three parts. The fourth part of the logical correlation pairs is divided into two parts. The fourth part of the logical correlation pairs is divided into three parts. The fourth part of the logical correlation pairs is divided into three parts. The fourth part is (Ordered) tree-shellable, effective and double matching, etc., the use of special features may not be possible, and the determination of whether these features belong to the category is necessary. Quadratic relations (the number of products of the product sum expression is 2) are determined for polynomial time. In general cases, the number of products of the product sum expression is 2. The number of relations is (ordered) tree-shellfish. The necessary conditions are shown. In the previous year, the number of changes in the number of changes.