Mathematical Sciences: Algorithmic Problems in Groups and Semigroups

9623284 Meakin这笔赠款支持Meakin教授、MarGolis教授、Sapir教授和Birget教授研究群和半群的算法和计算理论中的一系列问题。第一个领域是群和半群的Dehn函数与关联字问题的计算复杂性之间的关系。下一个目标是进一步研究与半群表示相关的图群的性质。第三个领域是重写各类群和半群的系统。第四个领域是自动机的扩张问题。最后是群变种理论中各种算法问题的研究。这是群和半群理论领域的研究。这些领域可以被认为是对抽象对称性的研究。因此，这个领域在物理和化学的许多领域都有直接的应用。此外，在过去的30年里，使用群论的技术解决了许多与数据传输中的问题有关的问题。还有与纠错码的直接联系，这些纠错码对现代计算至关重要，例如使用CD-ROM以及一般的理论计算机科学。

9623284 Meakin This grant supports the research of Professors Meakin, Margolis, Sapir and Birget to work on a series of problems in the algorithmic and computational theory of groups and semigroups. The first area is the relationship between Dehn functions of groups and semigroups and the computational complexity of the associated word problem. The next goal is to study further the properties of diagram groups associated with semigroup presentations. The third area is that of rewriting systems for various classes of groups and semigroups. The fourth area is extension problems for automata. The final area is the study of various algorithmic problems in the theory of group varieties. This is research in the field of group and semigroup theory. These areas can be thought of as the study of symmetry in the abstract. As such, this area has direct applications to many areas of physics and chemistry. Moreover, within the last 30 years, many connections to problems in data transmission have been solved using techniques from group theory. There are also direct connections to the error correcting codes that are vital for modern computing such as working with CD-ROM's as well as to theoretical computer science in general.