Logics for Unordered Trees with Data Constraints on Siblings

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.