In [3], we introduced a framework for querying and updating probabilistic information over unordered labeled trees, the probabilistic tree model. The data model is based on trees where nodes are annotated with conjunctions of probabilistic event variables. We briefly described an implementation and scenarios of usage. We develop here a mathematical foundation for this model. In particular, we present complexity results. We identify a very large class of queries for which simple variations of querying and updating algorithms from [3] compute the correct answer. A main contribution is a full complexity analysis of queries and updates. We also exhibit a decision procedure for the equivalence of probabilistic trees and prove it is in co-rp. Furthermore, we study the issue of removing less probable possible worlds, and that of validating a probabilistic tree against a DTD. We show that these two problems are intractable in the most general case.
They also gave a full complexity analysis of querying and updating on the "fuzzy trees" in REF .
On the complexity of managing probabilistic XML data
PODS '07
Computer Science