Decidability of Downward XPath
ACM Transactions on Computational Logic (TOCL)
On XPath with transitive axes and data tests
Proceedings of the 32nd symposium on Principles of database systems
Extending two-variable logic on data trees with order on data values and its automata
ACM Transactions on Computational Logic (TOCL)
Reasoning about Data Repetitions with Counter Systems
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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We study the satisfiability problem for a logic on data words. A data word is a finite word where every position carries a label from a finite alphabet and a data value from an infinite domain. The logic we consider is two-way, contains future and past modalities, which are considered as reflexive and transitive relations, and data equality and inequality tests. This logic corresponds to the fragment of XPath with the 'following-sibling-or-self' and 'preceding-sibling-or-self' axes over data words. We show that this problem is decidable, EXPSPACE-complete. This is surprising considering that with the strict (non-reflexive) navigation relations the satisfiability problem is undecidable. To prove this, we first reduce the problem to a derivation problem for an infinite transition system, and then we show how to abstract this problem into a reachability problem of a finite transition system.