The language complexity of problems in algebra and logic

这个项目集中在代数、逻辑和计算机科学的交集上的一个主要问题，关于自由群和自由么半群上的方程。预期的结果包括从语言理论上描述一大类群和么半群中的方程的解，从语言理论上理解自由群的存在理论和一阶理论，以及使用索引乘法表和EDT0L应用题对群进行分类。该项目旨在扩大理论计算机科学和纯数学方面的知识前沿，但从长远来看，是为了加深我们对计算机及其计算能力和内在局限性的理解。

This project focuses on a major problem at the intersection of algebra, logic and computer science, concerning equations over free groups and free monoids. Expected outcomes include a language-theoretic characterisation of solutions of equations in a wide class of groups and monoids, a language-theoretic understanding of the existential and first-order theories of free groups, and a classification of groups with indexed multiplication tables and EDT0L word problem. The project is designed to expand the frontiers of knowledge in theoretical computer science and pure mathematics, but in the longer term to deepen our understanding of computers, their computational power and intrinsic limitations.