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Journal of Software:2011.22(6):1169-1184

循环对称化简及在三值模型上的扩展
魏欧,袁泳,蔡昕烨,黄志球,徐丙凤
(南京航空航天大学 计算机科学与技术学院,江苏 南京 210016;Department of Computer Science, University of Toronto, Ontario Canada M5S 3G4)
Cycle Symmetry Reduction and Its Extension on Three-Valued Models
WEI Ou,YUAN Yong,CAI Xin-Ye,HUANG Zhi-Qiu,XU Bing-Feng
(College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China; Department of Computer Science, University of Toronto, Ontario Canada M5S 3G4)
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Received:July 10, 2010    Revised:March 29, 2011
> 中文摘要: 为了将对称化简扩展到更多的非对称系统上,扩展了传统的基于自同构的对称性,提出了一种称为循环对称的新的对称性.证明了采用循环对称置换群或者由一组循环对称置换所生成的置换群仍可得到与原模型互模拟的对称商结构,从而达到化简系统规模的目的.进一步地,研究如何将对称化简应用于多值模型.多值模型可以有效地表示系统中的不确定信息,正越来越多地用于软件系统的建模与分析中.针对一种具体的多值模型——三值模型,定义传统的对称化简和循环对称化简在其上面的扩展.最后,分析三值模型的商结构与由约简得到的二值模型商结构之间的关系,证明了两种途径的等价性.
Abstract:This paper defines the notion of cycle symmetry, which extends the traditional automorphism-based symmetry and enables application of symmetry reduction to a broader class of asymmetric systems. The study also shows that both cycle symmetry group and cycle symmetry generated group can be used to produce a quotient structure that is bisimilar to the original model. Furthermore, the extension of symmetry reduction over three-valued models is investigated. The quotient structure of a three-valued model is defined and induced by a permutation group and extends to both automorphism-based symmetry reduction and cycle symmetry reduction to three-valued models. Finally, the study analyzes the relationship between symmetry reduction of a three-valued model and classical models induced by it. Both approaches can lead to the same reduced quotient structure of the original model.
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基金项目:国家高技术研究发展计划(863)(2009AA010307); 中国博士后科学基金(20100471338); 南京航空航天大学基本科研业务费专项科研项目(NS2010110) 国家高技术研究发展计划(863)(2009AA010307); 中国博士后科学基金(20100471338); 南京航空航天大学基本科研业务费专项科研项目(NS2010110)
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魏欧,袁泳,蔡昕烨,黄志球,徐丙凤.循环对称化简及在三值模型上的扩展.软件学报,2011,22(6):1169-1184

WEI Ou,YUAN Yong,CAI Xin-Ye,HUANG Zhi-Qiu,XU Bing-Feng.Cycle Symmetry Reduction and Its Extension on Three-Valued Models.Journal of Software,2011,22(6):1169-1184