Isoperimetric functions of groups and computational complexity of the word problem

• 成果类型: Article
• 署名作者: Birget, JC; Ol'shanskii, AY; Rips, E; Sapir, MV
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/3597196
• 发表日期: 2002
• 页码: 467-518
• 关键词: INEQUALITIES

摘要

We prove that the word problem of a finitely generated group G is in NP (solvable in polynomial time by a nondeterministic Turing machine) if and only if this group is a subgroup of a finitely presented group H with polynomial isoperimetric function. The embedding can be chosen in such a way that G has bounded distortion in H. This completes the work started in [6] and [25].