[irmfvkbq] Musing about Burrows-Wheeler

I remain surprised that the Burrows-Wheeler transform is reversible.

Create a formal proof.  Given a formal description of the forward direction of the transform, automatically derive an efficient algorithm for the reverse.

What is the order of repeated applications of the forward transform?  Can we exponentiate quickly a la Diffie-Hellman?  Calculate roots and discrete logarithms?

It looks like both the forward and reverse transforms can be repeatedly applied as long as one considers them as circular permutations acting on circular strings.