Well-structured transition systems everywhere!
Theoretical Computer Science
Efficient algorithms for processing XPath queries
ACM Transactions on Database Systems (TODS)
Two-variable logic on data trees and XML reasoning
Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
The expressivity of XPath with transitive closure
Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
LTL with the Freeze Quantifier and Register Automata
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
XPath satisfiability in the presence of DTDs
Journal of the ACM (JACM)
XPath, transitive closure logic, and nested tree walking automata
Proceedings of the twenty-seventh ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Satisfiability of downward XPath with data equality tests
Proceedings of the twenty-eighth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Future-Looking Logics on Data Words and Trees
MFCS '09 Proceedings of the 34th International Symposium on Mathematical Foundations of Computer Science 2009
Satisfiability of XPath queries with sibling axes
DBPL'05 Proceedings of the 10th international conference on Database Programming Languages
Two-variable logic and key constraints on data words
Proceedings of the 14th International Conference on Database Theory
On the complexity of tree pattern containment with arithmetic comparisons
Information Processing Letters
Foundations of XML based on logic and automata: a snapshot
FoIKS'12 Proceedings of the 7th international conference on Foundations of Information and Knowledge Systems
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
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We consider a fragment of XPath named 'forward-XPath', which contains all descendant and rightwards sibling axes as well as data equality and inequality tests. The satisfiability problem for forward-XPath in the presence of DTDs and even of primary key constraints is shown here to be decidable. To show decidability we introduce a model of alternating automata on data trees that can move downwards and rightwards in the tree, have one register for storing data and compare them for equality, and have the ability to (1) non-deterministically guess a data value and store it, and (2) quantify universally over the set of data values seen so far during the run. This model extends the work of Jurdziński and Lazić. Decidability of the finitary non-emptiness problem for this model is obtained by a direct reduction to a well-structured transition system, contrary to previous approaches.