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.

  • $\begingroup$ Jeff, I got your email and replied. If you do not get my reply, please let me know, here I guess. I made this a "favorite" question, I will automatically be able to find this. $\endgroup$ – Will Jagy Sep 26 '11 at 4:44
  • $\begingroup$ Braid group based cryptography was popular at the very beginning of the 21st century when the Anshel-Anshel-Goldfeld key exchange was originally invented, but today people view braid group cryptography as insecure. $\endgroup$ – Joseph Van Name Apr 25 '17 at 16:11

The group-based cryptography is a very active area now. There are books and a special journal.

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 this paper).

Small cancelation itself is not used much in any of these areas, but many ideas are inspired by the classical small cancelation theory.


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