Efficient evaluation for a temporal logic on changing XML documents

We consider a sequence t₁,...,t_k of XML documents that is produced by a sequence of local edit operations. To describe properties of such a sequence, we use a temporal logic. The logic can navigate both in time and in the document, e.g. a formula can say that every node with label a eventually gets a descendant with label b. For every fixed formula, we provide an evaluation algorithm that works in time O(k ⋅ log(n)), where k is the number of edit operations and n is the maximal size of document that is produced. In the algorithm, we represent formulas of the logic by a kind of automaton, which works on sequences of documents. The algorithm works on XML documents of bounded depth.