Mathematical Modeling of Ubiquitous Systems

摘要：

Ubiquitous systems built in the environment of distributed or parallel computing are more complicated than conventional digital systems. This paper describes how ubiquitous systems are modeled mathematically or in a formal way using the incrementally modular abstraction hierarchy. Firstly, the system requirements represented by event sequences are mathematically expressed by the Cartesian product of actors and events using a fiber bundle. Then, the fiber bundles is lifted by the homotopy lifting property to the set of subspaces, each of which describes the behavior of a part of the system. This property is used for modeling the ubiquitous system in a bottom-up way. Assembling behaviors distributed in parts of the system, the behavior of an actor is defined by the homotopy extension property for modeling the system in a top-down way. Finally, the behaviors of the actors are adjoined together by attaching functions to express the system behavior, which is equivalent to the process obtained by process algebra. The problem of process algebra not having the methodology of how the system is modeled from system requirements to formal description is solved by the proposed incrementally modular abstraction hierarchy.

关键词： Homotopy incrementally modular abstraction hierarchy process algebra system development

作者: Kenji Ohmori Tosiyasu L. Kunii

作者单位: Computer and Information Sciences Hosei University 3-7-2 Kajino-cho,Koganei-shi Tokyo 184-8584 Japan Morpho,Inc.The University of Tokyo,Entrepreneur Plaza 7-3-1 Hongo,Bunkyo-ku,Tokyo 113-0033 Japan

会议类型: 国际会议

会议名称: The First IEEE International Conference on Ubi-Media Coputing and Workshops(第一届泛媒体处理国际会议)

会议地点: 兰州

会议语种:英文

在线出版日期: 2008-07-15（万方平台首次上网日期，不代表论文的发表时间）