Isoperimetric Functions of Groups and Computational Complexity of the Word Problem

Research paper by J. -C. Birget, A. Yu. Olshanskii, E. Rips, M. Sapir

Indexed on: 17 Nov '98Published on: 17 Nov '98Published in: Mathematics - Group Theory


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 $H$.