基于节点分类的概念格同构判定算法

概念格的同构判定问题是机器学习、知识工程等领域的一个研究重点,广泛应用。针对现有同构判定算法时间复杂度较高的问题,提出一种基于节点分类的概念格同构判定算法,以期利用同构判定算法中只需要处理一种类型节点的特性,缩减搜索空间,提高算法效率。首先,算法引入节点分层方法,结合节点的入度和出度,将其分为4种类型,并创建等价类;然后,以对应等价类为基本处理单元,调用EquivalenceClass算法找出节点的映射。仿真实验结果表明,该算法具有较低时间复杂度,在确保算法有效性的基础上提高了处理效率。     

无向图的层次化谱分析同构判定算法

针对无向图同构的判定问题,一种层次化的基于谱分析的同构判定算法.比较两图的顶点数、边数以及度数序列对图进行预同构判定;然后对具有唯一Fiedler向量的图通过层次化的谱分析算法进行再次同构判定.与最具代表性的同构判定算法Nauty相比,随着判定图的规模增大,该算法对于规则网格图和固定度数图具有更高的同构判定效率.     

基于OBDD的SMC中PRE 操作的改进算法

提出一种基于排序二值判定图（OBDD）的符号模型检测中PRE 操作的改进算法。该算法处理PRE 步骤3（嵌套布尔存在量化）的方法是一次遍历“删除”所有被量化变量的节点,产生表示布尔函数与嵌套存在量化结果等价的不确定排序二值判定图,把不确定排序二值判定图转换成OBDD。实验表明,该算法能有效缩短计算时间,减少中间节点所需空间。     

基于OBDD的SMC中PRE(E)操作的改进算法

提出一种基于排序二值判定图(OBDD)的符号模型检测中PRE(操作的改进算法.该算法处理PRE(步骤3(嵌套布尔存在量化)的方法是一次遍历"删除"所有被量化变量的节点,产生表示布尔函数与嵌套存在量化结果等价的不确定排序二值判定图,把不确定排序二值判定图转换成OBDD.实验表明,该算法能有效缩短计算时间,减少中间节点所需空间.     

一种基于子图近似同构的e-Learning学习资源本体匹配方法

针对e-Learning学习资源本体异构问题, 提出一种基于子图近似同构的本体匹配方法。该方法对现有本体匹配方法进行扩展, 综合编辑距离、层次关系等特征, 计算本体的结构级相似性, 以点、边有序交替匹配来判断实体的有向图近似同构问题, 实现本体匹配判定。演示算法处理过程, 给出算法时间复杂度理论分析, 说明其有效性。     

基于OBDD的SMC中PRE操作的改进算法

提出一种基于排序二值判定图(OBDD)的符号模型检测中PRE操作的改进算法。该算法处理PRE步骤3(嵌套布尔存在量化)的方法是一次遍历“删除”所有被量化变量的节点,产生表示布尔函数与嵌套存在量化结果等价的不确定排序二值判定图,把不确定排序二值判定图转换成OBDD。实验表明,该算法能有效缩短计算时间,减少中间节点所需空间。     

基于二元决策图的网络可靠性评估

提出一种改进-二元决策图(BDD)的网络可靠性评估方法.为了解决BDD构造中有效识别同构子图的问题,将边收缩/删除法应用于BDD的图分解中,并提出了BDD的宽度优先搜索算法,通过遍历BDD图对边进行排序,为布尔函数的不交化提供了一种新的高效途径.实验结果表明,该算法具有精确性高、时间复杂度低的优点,可以避免常规最小路算...     

布尔函数表示的二元判定图方法的研究与实现

布尔函数是数字系统与计算机科学等领域的基础，有广泛的应用。本文对布尔函数的二元判定图表示方法进行了详细讨论，说明了基于布尔函数的真值表和香农展开式来构造二元判定图的方法、二元判定图的简化、以及它在数字电路设计与测试中的应用。     

基于OBDD的描述逻辑εL循环术语集推理

循环术语集推理是描述逻辑研究中面临的难点问题,尚未得到很好的解决.有序二叉决策图（ordered binary decision diagram,简称OBDD）是一种对布尔函数进行紧凑表示和高效操作的数据结构,适用于表示和处理大规模问题.将OBDD应用于描述逻辑循环术语集的推理.首先,针对描述逻辑εL中的循环术语集,给出了描述图上关于最大模拟关系的重要性质,并借助集合表示和集合运算对该性质进行了表述和证明.在此基础上,应用布尔函数对描述图进行编码,给出了基于OBDD求解最大模拟关系的方法,进而给出了最大不动点语义下基于OBDD对概念包含关系进行判定的算法;接下来,基于OBDD给出了求解描述图中可以到达循环路径的所有结点的方法,进而给出了最小不动点语义下基于OBDD对概念包含关系进行判定的算法;最后,对算法的正确性、复杂度等进行了分析和证明,并对算法进行了编程实现,给出了关于计算性能的实验结果.该工作为循环术语集的推理提供了一条有效途径,也为OBDD在逻辑推理中的应用提供了新的案例.     

形式背景同构判定的等价类算法

同构生成概念格是获取概念格的另一途径，而形式背景同构判定是这一方法的前提，也是决定整个算法时间复杂度的关键。本文提出的基于等价类法的形式背景同构判定算法，有效地提高了同构判定的效率。结合形式背景的分解和约简等手段，为概念格的构造提供了一种有实用价值的方法。本文对该方法的原理和算法设计进行了较详细的讨论，并通过实验，验证了算法的正确性和有效性。     

The influence of oppositely classified examples on the generalization complexity of Boolean functions

In this paper, we analyze Boolean functions using a recently proposed measure of their complexity. This complexity measure, motivated by the aim of relating the complexity of the functions with the generalization ability that can be obtained when the functions are implemented in feed-forward neural networks, is the sum of a number of components. We concentrate on the case in which we use the first two of these components. The first is related to the "average sensitivity" of the function and the second is, in a sense, a measure of the "randomness" or lack of structure of the function. In this paper, we investigate the importance of using the second term in the complexity measure, and we consider to what extent these two terms suffice as an indicator of how difficult it is to learn a Boolean function. We also explore the existence of very complex Boolean functions, considering, in particular, the symmetric Boolean functions.     

布尔函数的复杂系数及其应用

本文利用线性复杂度相关理论，给出了布尔函数复杂系数的定义：得出任何布尔函数的线性复杂度均等于这个函数的复杂系数；给出了一种快速求解布尔函数多项式表示的算法；研究了Bent函数的线性复杂度特点，利用布尔函数的复杂系数，得出布尔函数为Bent函数的一个必要条件。     

Maiorana-McFarland’s Bent函数零化子空间维数

在流密码和分组密码的设计中,所用布尔函数应该具有好的密码学性质来抵抗已知的各种有效攻击.布尔函数的低次零化子空间维数与其补函数低次零化子空间维数之和是评价该函数抵抗代数攻击能力的一个重要参数.根据Maiorana-McFarlands(M-M)Bent函数和布尔置换之间的一一对应关系,给出了一组布尔函数组并证明了它们是线性无关的.借助所给的线性无关布尔函数组和布尔置换中向量函数非零线性组合均是平衡函数的特性,给出了一类特殊M-M Bent函数低次零化子空间的维数与其补函数低次零化子空间的维数之和的一个上限.就这类特殊M-M Bent函数而言,该上限低于已知的限.进一步给出了适合所有M-M Bent函数的新上限.     

Larger lower bounds on the OBDD complexity of integer multiplication

Integer multiplication as one of the basic arithmetic functions has been in the focus of several complexity theoretical investigations and ordered binary decision diagrams (OBDDs) are one of the most common dynamic data structures for Boolean functions. Recently, the question whether the OBDD complexity of the most significant bit of integer multiplication is exponential has been answered affirmatively. In this paper a larger general lower bound is presented using a simpler proof. Furthermore, we prove a larger lower bound for the variable order assumed to be one of the best ones for the most significant bit. Moreover, the best known lower bound on the OBDD complexity for the so-called graph of integer multiplication is improved.     

On the minimization of complexity and automation of efficient representation of boolean functions in classes of formulas and circuits

A method for synthesizing Boolean formulas intended for the efficient construction of circuit composed on functional elements, which is also suitable for minimal complexity circuits, is developed. Upper bounds on the implementation complexity of arbitrary Boolean functions in terms of the Zhegalkin basis are determined. A computational method for improving these bounds is proposed. A method for deriving certain countable classes of Boolean functions of minimal complexity is also recommended.     

The Complexity of the Descriptiveness of Boolean Circuits over Different Sets of Gates

Any Boolean function can be defined by a Boolean circuit, provided we may use sufficiently strong functions in its gates. On the other hand, what Boolean functions can be defined depends on these gate functions: Each set B of gate functions defines the class of Boolean functions that can be defined by circuits over B. Although these classes have been known since the 1920s, their computational complexity was never investigated.In this paper we will study how difficult it is to decide for a Boolean function f and a class B, whether f is in B.Moreover, we will provide such a decision algorithm with additional information: How difficult is it to decide whether or not f is in B, provided we already know a circuit for f, but with gates from another class A? Given such a circuit, we know that f is in A. Is the problem harder if we do not have a concrete representation for f, but still know that it is from A? For nearly all possible combinations, we show that this is not the case, and that the problem is either in P or coNP-complete.     

The complexity of monotone boolean functions

We study the realization of monotone Boolean functions by networks. Our main result is a precise version of the following statement: the complexity of realizing a monotone Boolean function ofn arguments is less by the factor (2/n)^1/2, where is the circular ratio, than the complexity of realizing an arbitrary Boolean function ofn arguments. The proof combines known results concerning monotone Boolean functions with new methods relating the computing abilities of networks and machines.     

Extracting rules from trained neural networks

Presents an algorithm for extracting rules from trained neural networks. The algorithm is a decompositional approach which can be applied to any neural network whose output function is monotone such as a sigmoid function. Therefore, the algorithm can be applied to multilayer neural networks, recurrent neural networks and so on. It does not depend on training algorithms, and its computational complexity is polynomial. The basic idea is that the units of neural networks are approximated by Boolean functions. But the computational complexity of the approximation is exponential, and so a polynomial algorithm is presented. The author has applied the algorithm to several problems to extract understandable and accurate rules. The paper shows the results for the votes data, mushroom data, and others. The algorithm is extended to the continuous domain, where extracted rules are continuous Boolean functions. Roughly speaking, the representation by continuous Boolean functions means the representation using conjunction, disjunction, direct proportion, and reverse proportion. This paper shows the results for iris data.     

Unbounded-error quantum query complexity

This work studies the quantum query complexity of Boolean functions in an unbounded-error scenario where it is only required that the query algorithm succeeds with a probability strictly greater than 1/2. We show that, just as in the communication complexity model, the unbounded-error quantum query complexity is exactly half of its classical counterpart for any (partial or total) Boolean function. Moreover, connecting the query and communication complexity results, we show that the “black-box” approach to convert quantum query algorithms into communication protocols by Buhrman-Cleve—Wigderson [STOC’98] is optimal even in the unbounded-error setting.We also study a related setting, called the weakly unbounded-error setting, where the cost of a query algorithm is given by q+log(1/2(p−1/2)), where q is the number of queries made and p>1/2 is the success probability of the algorithm. In contrast to the case of communication complexity, we show a tight multiplicative Θ(logn) separation between quantum and classical query complexity in this setting for a partial Boolean function. The asymptotic equivalence between them is also shown for some well-studied total Boolean functions.