Dynamic algorithms for graphs of bounded treewidth

The formalism of monadic second-order (MS) logic has been very successful in unifying a large number of algorithms for graphs of bounded treewidth. We extend the elegant framework of MS logic from static problems to dynamic problems, in which queries about MS properties of a graph of bounded treewidth are interspersed with updates of vertex and edge labels. This allows us to unify and occasionally strengthen a number of scattered previous results obtained in an ad hoc manner and to enable solutions to a wide range of additional problems to be derives automatically. As an auxiliary result of independent interest, we dynamize a data structure of Chazelle for answering queries about products of labels along paths in a tree with edges labeled by elements of a semigroup.