  In this article, we propose tree edit distance with variables, which is an
extension of the tree edit distance to handle trees with variables and has a
potential application to measuring the similarity between mathematical
formulas, especially, those appearing in mathematical models of biological
systems. We analyze the computational complexities of several variants of this
new model. In particular, we show that the problem is NP-complete for ordered
trees. We also show for unordered trees that the problem of deciding whether or
not the distance is 0 is graph isomorphism complete but can be solved in
polynomial time if the maximum outdegree of input trees is bounded by a
constant. This distance model is then extended for measuring the
difference/similarity between two systems of differential equations, for which
results of preliminary computational experiments using biological models are
provided.
