Generic-case complexity, decision problems in group theory, and random walks

被引：148

作者：

Kapovich, I

Myasnikov, A

Schupp, P

Shpilrain, V

机构：

[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA

[2] CUNY City Coll, Dept Math, New York, NY 10031 USA

来源：

JOURNAL OF ALGEBRA | 2003年 / 264卷 / 02期

关键词：

D O I：

10.1016/S0021-8693(03)00167-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a precise definition of "generic-case complexity" and show that for a very large class of finitely generated groups the classical decision problems of group theory-the word, conjugacy, and membership problems-all have linear-time generic-case complexity. We prove such theorems by using the theory of random walks on regular graphs. (C) 2003 Elsevier Science (USA). All rights reserved.

引用

页码：665 / 694

页数：30

共 65 条

[1] Decision problems for groups and semigroups [J].