Complexity in Algebra and Algebra in Complexity: the role of finite semigroups and general algebra

代数和逻辑构成了表示和分析算法及其难度的数学框架。然后，我们可以科学地分析是什么让某些任务比其他任务更困难。这个项目统一了代数的平行领域，集中在代数和计算复杂性之间的这个交界处的两个关键主题上。作为进一步的工作，我们的工作可以发现解决约束问题和学习形式语言的新算法。 随着一个由国际顶尖研究人员组成的团队开发数学和算法研究之间的新互动，该项目将培养创新文化，并使澳大利亚在这个具有国际竞争力的领域发挥作用。

Algebra and logic form the mathematical framework for expressing and analysing algorithms and their difficulty. We can then scientifically analyse what makes some tasks more difficult than others. This project unifies parallel areas of algebra to focus on two key topics at this interface between algebra and computational complexity. As a flow on, our work can uncover new algorithms for solving constraint problems and for the study of formal languages. With a team of top international researchers developing new interactions between mathematics and the study of algorithms, the project will foster a culture of innovation and bring Australia into the play in this internationally competitive area.