  We are given three strings s, t, and t' of length L over some fixed finite
alphabet and an integer m that is polylogarithmic in L. We have a symmetric
relation on substrings of constant length that specifies which substrings are
allowed to be replaced with each other. Let Delta(n) denote the difference
between the numbers of possibilities to obtain t from s and t' from s after n
replacements. The problem is to determine the sign of Delta(m).
  As promises we have a gap condition and a growth condition. The former states
that |Delta(m)| >= epsilon c^m where epsilon is inverse polylogarithmic in L
and c>0 is a constant. The latter is given by Delta(n) <= c^n for all n.
  We show that this problem is PromiseBQP-complete, i.e., it represents the
class of problems which can be solved efficiently on a quantum computer.
