Complexity of group algorithms and statistical fingerprints of groups

该项目的目的是在群论，对称数学领域塑造下一代高效的随机算法。基础数学支撑着现代技术任务，如网络搜索，排序和数据压缩。该项目旨在确定关键构件组的特征统计指纹。这些组统计数据导致更快的过程，以类似于将整数分解为其素因子的方式将巨大的组分解为较小的构建块组。预期的目标是将结果包括在公开可用的符号代数计算机包中。由于对称性理论在数学和物理科学中有着广泛的应用，因此有可能带来深远的利益。

This project aims to shape the next generation of efficient randomised algorithms in the field of group theory, the mathematics of symmetry. Fundamental mathematics underpins modern technological tasks such as web searches, sorting and data compression. This project aims to determine characteristic statistical fingerprints of key building-block groups. These group statistics lead to much faster procedures to essentially factor huge groups into smaller building-block groups in a manner akin to factoring an integer into its prime factors. The anticipated goal is to include the outcomes in publicly available symbolic algebra computer packages. As the theory of symmetry has broad applications in the mathematical and physical sciences, there is the potential for far reaching benefits.