Isoperimetric Functions of Groups and Computational Complexity of the Word Problem
J. -C. Birget, A. Yu. Olshanskii, E. Rips, M. Sapir
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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