Isoperimetric functions of groups and computational complexity of the word problem

J. C. Birget; A. Yu Ol'shanskii; E. Rips; M. V. Sapir

doi:10.2307/3597196

Isoperimetric functions of groups and computational complexity of the word problem

J. C. Birget^*, A. Yu Ol'shanskii, E. Rips, M. V. Sapir

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

43 Scopus citations

Abstract

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].

Original language	English
Pages (from-to)	467-518
Number of pages	52
Journal	Annals of Mathematics
Volume	156
Issue number	2
DOIs	https://doi.org/10.2307/3597196
State	Published - Sep 2002

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abstract = "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].",

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Isoperimetric functions of groups and computational complexity of the word problem

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