Before revision:  In this work, we  introduce the first fully polynomial time randomized approximation scheme (FPRAS) for counting the number of trees of size n accepted by a tree automaton, where n is given in unary , and the first polynomial time algorithm for sampling uniformly from this set of trees.
After revision:  In this work, we introduce the first fully polynomial time randomized approximation scheme (FPRAS) for counting answers to a query in C , and the first polynomial time algorithm for sampling uniformly from this set of trees.