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In this article, we propose tree edit distance with variables, which is anextension of the tree edit distance to handle trees with variables and has apotential application to measuring the similarity between mathematicalformulas, especially, those appearing in mathematical models of biologicalsystems. We analyze the computational complexities of several variants of thisnew model. In particular, we show that the problem is NP-complete for orderedtrees. We also show for unordered trees that the problem of deciding whether ornot the distance is 0 is graph isomorphism complete but can be solved inpolynomial time if the maximum outdegree of input trees is bounded by aconstant. This distance model is then extended for measuring thedifference/similarity between two systems of differential equations, for whichresults of preliminary computational experiments using biological models areprovided.

Tree Edit Distance with Variables. Measuring the Similarity between Mathematical Formulas