Mike Stay asked
>
>Given a basis for a group, can one calculate in polynomial time how far
>apart two states are? How about finding a shortest path between two
>states? Does anyone know good search terms to find papers on this sort
>of thing?
>--
Not sure if this is what you are looking for, but a specific variant
of this problem is computation of the so-called "Levenstein Distance".
If you go (for example) to www.google.com and use that to search
on this phrase, you will be pointed to a number of pages that talk
about it.
Use of this algorithm is mainly in the context of seeing
"how close" one alpha string is to another (see
http://w3.nai.net/~rvdi/lDistance/index.html for example) although
this has then been used as an underpinning to measure "distance"
between finger-prints and so forth.
On further thought - I doubt that this is what you are looking
for, but it might serve as a jumping point for references to
other work related to the more general problem.
Jitze
