Abstract
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 derived automatically.As an auxiliary result of independent interest, we dynamize a data structure of Chazelle and Alon and Schieber for answering queries about sums of labels along paths in a tree with edges labeled by elements of a semigroup.KeywordsQuery TimeSpringer Lecture NoteRing AttributeTree AutomatonLower Common AncestorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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