Logics for Unordered Trees with Data Constraints on Siblings

Abstract

We study counting monadic second-order logics (CMso) for unordered data trees. Our objective is to enhance this logic with data constraints for comparing string data values attached to sibling edges of a data tree. We show that CMso satisfiability becomes undecidable when adding data constraints between siblings that can check the equality of factors of data values. For more restricted data constraints that can only check the equality of prefixes, we show that it becomes decidable, and propose a related automaton model with good complexities. This restricted logic is relevant to applications such as checking well-formedness properties of semi-structured databases and file trees. Our decidability results are obtained by compilation of CMso to automata for unordered trees, where both are enhanced with data constraints in a novel manner.

Automata for unordered trees

“…We also have a set D of data values, which in all our applications are words over a finite alphabet ∆ so that D = ∆ * . However, the internal word structure of data values, while convenient for examples, is not essential to the theory developed in this paper, unlike in [31], and we can generally see D merely as some infinite alphabet. Those data values will be used as labels for the edges of the trees.…”

Grammar-Based Compression of Unranked Trees

“…is particularly effective for XML document trees (see [14]), and (ii) XML document trees can often be considered unordered (one speaks of "data-centric XML", see e.g. [1,3,5,19,20]), allowing even stronger grammar-based compressions [16].…”