TITLE: Any nice examples of small cancellation theory appearing in applied mathematics?
QUESTION [9 upvotes]: Are there any nice discussions of applications of small cancellation theory, or other cases of the word problem, in applied mathematics or algorithms for seemingly non-group theoretic problems?  
I suppose two candidates are Anshel–Anshel–Goldfeld key exchange and braid group based cryptography.

REPLY [6 votes]: The group-based cryptography is a very active area now. There are books (eg Group-based Cryptography) and a  special journal, Groups Complexity Cryptology.
As another application, one can reformulate the problem P=NP as "Is it true that every finitely presented group with polynomial Dehn function has word problem solvable deterministically in polynomial time?" (see the paper Isoperimetric and isodiametric functions of groups arXiv:math/9811105).
Small cancelation itself is not used much in any of these areas, but many ideas are inspired by the classical small cancelation theory.