Correspondence systems Given a list of pairs p with {u, v} = Transpose[p] the constraint to be satisfied is StringJoin[u 〚 s 〛 ]  StringJoin[v 〚 s 〛 ] Thus for example p = {{"ABB", "B"}, {"B", "BA"}, {"A", "B"}} has shortest solution s = {2, 3, 2, 2, 3, 2, 1, 1} . (One can have lists instead of strings, replacing StringJoin by Flatten .)