Recent advances in algorithmic problems for semigroups

Autor:	Dong, Ruiwen
Rok vydání:	2023
Předmět:	Computer Science - Discrete Mathematics Computer Science - Computational Complexity Mathematics - Group Theory
Druh dokumentu:	Working Paper
Popis:	In this article we survey recent progress in the algorithmic theory of matrix semigroups. The main objective in this area of study is to construct algorithms that decide various properties of finitely generated subsemigroups of an infinite group $G$, often represented as a matrix group. Such problems might not be decidable in general. In fact, they gave rise to some of the earliest undecidability results in algorithmic theory. However, the situation changes when the group $G$ satisfies additional constraints. In this survey, we give an overview of the decidability and the complexity of several algorithmic problems in the cases where $G$ is a low-dimensional matrix group, or a group with additional structures such as commutativity, nilpotency and solvability. Comment: survey article for SIGLOG News
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2309.10943 Zobrazit plný text záznamu View this record from Arxiv