Using the axiomatic method, abstract concepts such as abstract mean, abstract convex function and abstract majorization are proposed. They are the generalizations of concepts of mean, convex function and majorization,...Using the axiomatic method, abstract concepts such as abstract mean, abstract convex function and abstract majorization are proposed. They are the generalizations of concepts of mean, convex function and majorization, respectively. Through the logical deduction, the fundamental theorems about abstract majorization inequalities are established as follows: for arbitrary abstract mean Σ and $ \Sigma ' $ and abstract ∑ ? $ \Sigma ' $ strict convex function f(x) on the interval I, if x i , y i ∈ I (i = 1, 2,..., n) satisfy that $ (x_1 ,x_2 , \ldots ,x_n ) \prec _n^\Sigma (y_1 ,y_2 , \ldots ,y_n ) $ then $ \Sigma ' $ {f(x 1), f(x 2),..., f(x n )} ? $ \Sigma ' $ {f(y 1), f(y 2),..., f(y n )}. This class of inequalities extends and generalizes the fundamental theorem of majorization inequalities. Moreover, concepts such as abstract vector mean are proposed, the fundamental theorems about abstract majorization inequalities are generalized to n-dimensional vector space. The fundamental theorem of majorization inequalities about the abstract vector mean are established as follows: for arbitrary symmetrical convex set $ \mathcal{S} \subset \mathbb{R}^n $ , and n-variable abstract symmetrical $ \overline \Sigma $ ? $ \Sigma ' $ strict convex function $ \phi (\bar x) $ on $ \mathcal{S} $ , if $ \bar x,\bar y \in \mathcal{S} $ , satisfy $ \bar x \prec _n^\Sigma \bar y $ , then $ \phi (\bar x) \geqslant \phi (\bar y) $ ; if vector group $ \bar x_i ,\bar y_i \in \mathcal{S}(i = 1,2, \ldots ,m) $ satisfy $ \{ \bar x_1 ,\bar x_2 , \ldots ,\bar x_m \} \prec _n^{\bar \Sigma } \{ \bar y_1 ,\bar y_2 , \ldots ,\bar y_m \} $ , then $ \Sigma '\{ \phi (\bar x_1 ),\phi (\bar x_2 ), \ldots ,\phi (\bar x_m )\} \geqslant \Sigma '\{ \phi (\bar y_1 ),\phi (\bar y_2 ), \ldots ,\phi (\bar y_m )\} $ .展开更多
By means of the absolute continuities of the abstract functions whose values lie in X, the characterizations of Banach lattices X being 1-concave or satisfying lower p-estimates are obtained.
HEST is a practical integrated expert system tool. Its basis is a knowledge programming language FFLL, characterized by a combination of fuzzy logic and function paradigms. The tool integrates alot of important knowle...HEST is a practical integrated expert system tool. Its basis is a knowledge programming language FFLL, characterized by a combination of fuzzy logic and function paradigms. The tool integrates alot of important knowledge processing capabilities such as fuzzy reasoning, function computation, knowledge compilation and explanation, knowledge base maintenance, as well as practical programming functions, e.g., editing, filing, compiling, module imbedding, etc., constructing, a user--friendly knowledge application environment, HEST can enable expert system development in various domaills quickly and easily.This paper gives an outline of the design and implementation of HEST.展开更多
分析实际程序时往往需要分析程序中函数的调用,一般使用过程间分析来实现全程序分析.函数内联是一种最为精确、易于实现的过程间分析方法.通过函数内联,可以使得已有过程内分析方法和工具支持包含函数调用的程序的分析.但是函数内联后...分析实际程序时往往需要分析程序中函数的调用,一般使用过程间分析来实现全程序分析.函数内联是一种最为精确、易于实现的过程间分析方法.通过函数内联,可以使得已有过程内分析方法和工具支持包含函数调用的程序的分析.但是函数内联后代码的规模急剧增加,同时将产生大量中间变量,增加程序分析的变量维度,导致程序分析过程时空开销大大增加.考虑基于抽象解释框架下函数内联过程间分析的一些不足,并提出了相应的优化方法.基于抽象解释的程序分析关注自动推导程序变量之间的不变式约束关系,因此程序变量构成的程序环境大小(即各程序点处须考虑的相关变量集合)对分析的时空开销具有重要影响.为了减少函数内联后程序分析的开销,提出了面向内联函数块的程序环境降维优化方法.该方法针对内联函数后的程序代码,分析确定不同程序点处需维护的程序环境(即相关变量集合),而不是所有程序点共享同一全局程序环境,从而实现程序状态的降维.详细描述了基于该方法所实现的工具DRIP(dimension reduction for analyzing function inlined program)的架构、模块及算法细节.并在WCET Benchmarks测试集开展了分析实验.实验结果表明:DRIP在变量消除上取得的效果良好,甚至在某些测试集上能减少一半以上的变量,并在一定程度上降低了分析过程的时空开销.展开更多
基金supported by the National Key Basic Research Project of China (Grant No. 2004CB318003)the Foundation of the Education Department of Sichuan Province of China (Grant No. 07ZA087)
文摘Using the axiomatic method, abstract concepts such as abstract mean, abstract convex function and abstract majorization are proposed. They are the generalizations of concepts of mean, convex function and majorization, respectively. Through the logical deduction, the fundamental theorems about abstract majorization inequalities are established as follows: for arbitrary abstract mean Σ and $ \Sigma ' $ and abstract ∑ ? $ \Sigma ' $ strict convex function f(x) on the interval I, if x i , y i ∈ I (i = 1, 2,..., n) satisfy that $ (x_1 ,x_2 , \ldots ,x_n ) \prec _n^\Sigma (y_1 ,y_2 , \ldots ,y_n ) $ then $ \Sigma ' $ {f(x 1), f(x 2),..., f(x n )} ? $ \Sigma ' $ {f(y 1), f(y 2),..., f(y n )}. This class of inequalities extends and generalizes the fundamental theorem of majorization inequalities. Moreover, concepts such as abstract vector mean are proposed, the fundamental theorems about abstract majorization inequalities are generalized to n-dimensional vector space. The fundamental theorem of majorization inequalities about the abstract vector mean are established as follows: for arbitrary symmetrical convex set $ \mathcal{S} \subset \mathbb{R}^n $ , and n-variable abstract symmetrical $ \overline \Sigma $ ? $ \Sigma ' $ strict convex function $ \phi (\bar x) $ on $ \mathcal{S} $ , if $ \bar x,\bar y \in \mathcal{S} $ , satisfy $ \bar x \prec _n^\Sigma \bar y $ , then $ \phi (\bar x) \geqslant \phi (\bar y) $ ; if vector group $ \bar x_i ,\bar y_i \in \mathcal{S}(i = 1,2, \ldots ,m) $ satisfy $ \{ \bar x_1 ,\bar x_2 , \ldots ,\bar x_m \} \prec _n^{\bar \Sigma } \{ \bar y_1 ,\bar y_2 , \ldots ,\bar y_m \} $ , then $ \Sigma '\{ \phi (\bar x_1 ),\phi (\bar x_2 ), \ldots ,\phi (\bar x_m )\} \geqslant \Sigma '\{ \phi (\bar y_1 ),\phi (\bar y_2 ), \ldots ,\phi (\bar y_m )\} $ .
文摘By means of the absolute continuities of the abstract functions whose values lie in X, the characterizations of Banach lattices X being 1-concave or satisfying lower p-estimates are obtained.
文摘HEST is a practical integrated expert system tool. Its basis is a knowledge programming language FFLL, characterized by a combination of fuzzy logic and function paradigms. The tool integrates alot of important knowledge processing capabilities such as fuzzy reasoning, function computation, knowledge compilation and explanation, knowledge base maintenance, as well as practical programming functions, e.g., editing, filing, compiling, module imbedding, etc., constructing, a user--friendly knowledge application environment, HEST can enable expert system development in various domaills quickly and easily.This paper gives an outline of the design and implementation of HEST.
文摘分析实际程序时往往需要分析程序中函数的调用,一般使用过程间分析来实现全程序分析.函数内联是一种最为精确、易于实现的过程间分析方法.通过函数内联,可以使得已有过程内分析方法和工具支持包含函数调用的程序的分析.但是函数内联后代码的规模急剧增加,同时将产生大量中间变量,增加程序分析的变量维度,导致程序分析过程时空开销大大增加.考虑基于抽象解释框架下函数内联过程间分析的一些不足,并提出了相应的优化方法.基于抽象解释的程序分析关注自动推导程序变量之间的不变式约束关系,因此程序变量构成的程序环境大小(即各程序点处须考虑的相关变量集合)对分析的时空开销具有重要影响.为了减少函数内联后程序分析的开销,提出了面向内联函数块的程序环境降维优化方法.该方法针对内联函数后的程序代码,分析确定不同程序点处需维护的程序环境(即相关变量集合),而不是所有程序点共享同一全局程序环境,从而实现程序状态的降维.详细描述了基于该方法所实现的工具DRIP(dimension reduction for analyzing function inlined program)的架构、模块及算法细节.并在WCET Benchmarks测试集开展了分析实验.实验结果表明:DRIP在变量消除上取得的效果良好,甚至在某些测试集上能减少一半以上的变量,并在一定程度上降低了分析过程的时空开销.
