Efficient Computation in Finite Groups

本项目继续研究有限群的运算及其参数估计。有限群及其相关的Cayley图的算法在数学和计算机科学中有着广泛的应用。这些应用包括与有限单群的分类有关的问题、马尔可夫链的混合速度、大型相互作用的CPU阵列的互连网络的设计、(与化学文献相关的)图同构问题以及基于群的密码学(例如DES)。预期结果的主要消费者将是计算群论和算法复杂性理论领域；但在提到的其他领域也出现了应用。

This project continues research in the area of manipulation of finite groups and estimation of their parameters. Algorithms for finite groups and their associated Cayley graphs have a wide range of applications in mathematics and computer science. These applications range from problems related to the classification of finite simple groups to the mixing rate of Markov chains, the design of interconnection networks for large interacting arrays of CPU's, the graph isomorphism problem (of relevance to chemical documentation), and group-based cryptography (such as DES). The principal consumers of the expected results will be the areas of computational group theory and the complexity theory of algorithms; but applications arise in the other areas mentioned as well.