Recursive queries on trees and data trees

The analysis of datalog programs over relational structures has been studied in depth, most notably the problem of containment. The analysis problems that have been considered were shown to be undecidable with the exception of (i) containment of arbitrary programs in nonrecursive ones, (ii) containment of monadic programs, and (iii) emptiness. In this paper, we are concerned with a much less studied problem, the analysis of datalog programs over data trees. We show that the analysis of datalog programs is more complex for data trees than for arbitrary structures. In particular, we prove that the three aforementioned problems are undecidable for data trees. But in practice, data trees (e.g., XML trees) are often of bounded depth. We prove that all three problems are decidable over bounded depth data trees. Another contribution of the paper is the study of a new form of automata called pattern automata, that are essentially equivalent to linear datalog programs. We use pattern automata to show that the emptiness problem for linear monadic datalog programs with data value inequalities is decidable over arbitrary data trees.