Towards the Exact Minimization of BDDs—An Elitism-Based Distributed Evolutionary Algorithm

Binary Decision Diagrams (BDDs) are the state-of-the-art data structure for representation and manipulation of Boolean functions. In general, exact BDD minimization is NP-complete. For BDD-based technology, a small improvement in the number of nodes often simplifies the follow-up problem tremendously. This paper proposes an elitism-based evolutionary algorithm (EBEA) for BDD minimization. It can efficiently find the optimal orderings of variables for all LGSynth91 benchmark circuits with a known minimum size. Moreover, we develop a distributed model of EBEA, DEBEA, which obtains the best-ever variable orders for almost all benchmarks in the LGSynth91. Experimental results show that DEBEA is able to achieve super-linear performance compared to EBEA for some hard benchmarks.     

The temperature-composition phase diagram of the HgTe?HgI2 pseudobinary system on the HgTe rich side

The temperature-composition phase diagram of the HgTe? HgI₂ system was determined from 0 to 45 Mol-% HgI₂ between 25 and 670°C using Debye-Scherrer powder X-ray diffraction techniques and differential thermal analysis. Solid solutions of HgTe and HgI₂ with the cubic, zinc blende-type structure exist above 300°C, having a maximum solubility of 11.7 ± 0.8 Mol-% HgI₂ in HgTe at 501 ± 5°C. The known monoclinic compound Hg₃Te₂I₂ is formed by a peritectic reaction upon cooling at 501 ± 5°C, with the peritectic point at approximately 37 ± 4 Mol-% HgI₂.     

物理化学教材中表格数据的深度分析与教学实践——以电解质溶液一章为例

以电解质溶液一章为例,将物理化学教材中的表格数据进行多样化处理,结合离子电迁移率、迁移数以及平均活度因子等知识点,尝试运用数据补充、图象曲线处理、数据差值计算等方法,并进行综合应用,引导学生从更直观的角度主动思考和深入分析,从而加强对理论知识的理解。     

图表追踪的一种机器实现方法

交换图表追踪法是同调代数中一种重要的证明方法.本文提出了一种基于前推的交换图表追踪的机器实现方法,它可以证明同调代数中一系列基于交换图的定理.该方法从定理的结论出发,通过构造辅助元素以及对辅助元素进行推导,能在有限步内给出定理的证明.本文提出的前推方法已经在Java开发平台上实现,同调代数中的五引理、九引理、蛇引理等的证明都可以由我们的程序自动产生.     

Greechie Logics with Simple State Space Structure

We provide a simple algorithm for constructing Greechie logics whose states are convex linear combinations of two-valued states.     

映射的图可换性与模糊扩张原理

从映射的图可换角度对扩张原理进行解释。使得扩张原理更加直观，更易于理解，同时从图可换的角度研究张原理的若干性质及广义模糊扩张原理。     

Categorical abstract algebraic logic: The Diagram and the Reduction Operator Lemmas

The study of structure systems, an abstraction of the concept of first‐order structures, is continued. Structure systems have algebraic systems as their algebraic reducts and their relational component consists of a collection of relation systems on the underlying functors. An analog of the expansion of a first‐order structure by constants is presented. Furthermore, analogs of the Diagram Lemma and the Reduction Operator Lemma from the theory of equality‐free first‐order structures are provided in the framework of structure systems. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

命题逻辑公式的压缩表示及其相应的形式系统

提出一种将命题逻辑公式压缩表示的方法--公式的压缩图,给出相应的形式系统,并证明该系统的证明效率比传统相继式演算系统Gentzen\{cut}有指数级的提高,从而为命题逻辑提供了一种新的有效的推理系统.     

因果图法在仪器分析中的应用

通过分析影响仪器分析质量的5M1E因素,即操作者（Man）,仪器设备（Machine）,分析方法（Method）,分析材料（Material）,管理（Management）,环境（Environment）以及管理（management）,提出建立仪器分析的因果关系图的一般方法,并以原子吸收光谱分析中分析质量的因果关系为例,提出了提高仪器分析质量,减少分析误差的可行性控制措施.分别对因果关系图的绘制,应用和注意问题以及6大因素在仪器分析中的特点及防误措施作了介绍.     

Walker's Cancellation Theorem

Walker's cancellation theorem says that, if B ⊕ Z is isomorphic to C ⊕ Z in the category of abelian groups, then B is isomorphic to C. We construct an example in a diagram category of abelian groups where the theorem fails. As a consequence, the original theorem does not have a constructive proof even if B and C are subgroups of the free abelian group on two generators. Both of these results contrast with a group whose endomorphism ring has stable range one, which allows a constructive proof of cancellation and also a proof in any diagram category.