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Isoperimetric Functions of Groups and Computational Complexity of the Word Problem

J. -C. Birget·A. Yu. Olshanskii·E. Rips·M. Sapir
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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 non-deterministic 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 $H$.

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J. -C. Birget, A. Yu. Olshanskii, E. Rips, M. Sapir. 1998-11-18. Isoperimetric Functions of Groups and Computational Complexity of the Word Problem. https://arxiv.org/abs/math/9811106

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