Forward-XPath and extended register automata on data-trees
Proceedings of the 13th International Conference on Database Theory
Lossy counter machines decidability cheat sheet
RP'10 Proceedings of the 4th international conference on Reachability problems
Revisiting Ackermann-hardness for lossy counter machines and reset Petri nets
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Two-variable logic with two order relations
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
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
Computable fixpoints in well-structured symbolic model checking
Formal Methods in System Design
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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In a data word or a data tree each position carries a label from a finite alphabet and a data value from an infinite domain.Over data words we consider the logic ${\sf LTL}^{\downarrow}_{1}(\rm F)$, that extends LTL( F) with one register for storing data values for later comparisons. We show that satisfiability over data words of ${\sf LTL}^{\downarrow}_{1}(\rm F)$ is already non primitive recursive. We also show that the extension of ${\sf LTL}^{\downarrow}_{1}(\rm F)$ with either the backward modality F 驴 1 or with one extra register is undecidable. All these lower bounds were already known for ${\sf LTL}^{\downarrow}_{1}({\rm X,F})$ and our results essentially show that the X modality was not necessary.Moreover we show that over data trees similar lower bounds hold for certain fragments of Xpath.