• 论文 •

### 收敛无穷计算及其应用

1. 1. 北京航空航天大学 计算机科学与工程系;
2. 中国科学院 计算技术研究所
• 收稿日期:2002-06-12 出版日期:2002-05-31 发布日期:2010-09-25
• 作者简介:李 未(1943-),男,北京人,院士,100083,北京.
• 基金资助:

国家重点基础研究发展规划资助项目(G1999032701)

### Convergent Infinite Computation and Applications

LI Wei1, MA Shi-long1, SUI Yue-fei2, XU Ke1

1. 1. Beijing University of Aeronautics and Astronautics,Dept. of Computer Science and Engineering;
2. Chinese Academy of Sciences,Institute of Computing Technology
• Received:2002-06-12 Online:2002-05-31 Published:2010-09-25

Abstract: Classical computations can not capture the essence of infinite computations very well. This paper will focus on a class of infinite computations called convergent infinite computations and establish a logical framework for describing and analyzing how an infinite computation interacts and evolves in changing environments and what the limit of the evolution might be. A logic for convergent infinite computations was proposed by extending first order theories using Cauchy sequences,which has stronger expression power than the first order logic. A computation model,called procedure scheme,for convergent infinite computations was proposed,on the basis of classical Turing machine and formal theory sequences and their limits. It has stronger computing power than Turing machines and real machines in the sense of limit computations. As an example of application of the above study,the limit behavior of data mining was discussed by means of limits of theory sequences.