Presburger arithmetic with unary predicates is P11 complete
Journal of Symbolic Logic
Theoretical Computer Science
Languages, automata, and logic
Handbook of formal languages, vol. 3
On XML integrity constraints in the presence of DTDs
Journal of the ACM (JACM)
An Algebraic Characterization of Data and Timed Languages
CONCUR '01 Proceedings of the 12th International Conference on Concurrency Theory
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
XML with data values: typechecking revisited
Journal of Computer and System Sciences - Special issu on PODS 2001
ACM SIGMOD Record
Finite state machines for strings over infinite alphabets
ACM Transactions on Computational Logic (TOCL)
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
On the Complexity of Verifying Consistency of XML Specifications
SIAM Journal on Computing
A Decidable Temporal Logic of Repeating Values
LFCS '07 Proceedings of the international symposium on Logical Foundations of Computer Science
Optimizing Conjunctive Queries over Trees Using Schema Information
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
LTL with the freeze quantifier and register automata
ACM Transactions on Computational Logic (TOCL)
Automatic verification of data-centric business processes
Proceedings of the 12th International Conference on Database Theory
Two-variable logic on data trees and XML reasoning
Journal of the ACM (JACM)
Satisfiability of downward XPath with data equality tests
Proceedings of the twenty-eighth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Journal of Computer and System Sciences
Safety alternating automata on data words
ACM Transactions on Computational Logic (TOCL)
Two variables and two successors
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Automata vs. logics on data words
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Two-variable logic with two order relations
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
On the satisfiability of two-variable logic over data words
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Alternating automata on data trees and XPath satisfiability
ACM Transactions on Computational Logic (TOCL)
Two-variable logic on data words
ACM Transactions on Computational Logic (TOCL)
LICS '11 Proceedings of the 2011 IEEE 26th Annual Symposium on Logic in Computer Science
A Decidable Two-Way Logic on Data Words
LICS '11 Proceedings of the 2011 IEEE 26th Annual Symposium on Logic in Computer Science
On the complexity of equational horn clauses
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
Variable automata over infinite alphabets
LATA'10 Proceedings of the 4th international conference on Language and Automata Theory and Applications
Feasible automata for two-variable logic with successor on data words
LATA'12 Proceedings of the 6th international conference on Language and Automata Theory and Applications
Efficient reasoning about data trees via integer linear programming
ACM Transactions on Database Systems (TODS)
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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Data trees are trees in which each node, besides carrying a label from a finite alphabet, also carries a data value from an infinite domain. They have been used as an abstraction model for reasoning tasks on XML and verification. However, most existing approaches consider the case where only equality test can be performed on the data values. In this article we study data trees in which the data values come from a linearly ordered domain, and in addition to equality test, we can test whether the data value in a node is greater than the one in another node. We introduce an automata model for them which we call ordered-data tree automata (ODTA), provide its logical characterisation, and prove that its non-emptiness problem is decidable in 3-NExpTime. We also show that the two-variable logic on unranked data trees, studied by Bojanczyk et al. [2009], corresponds precisely to a special subclass of this automata model. Then we define a slightly weaker version of ODTA, which we call weak ODTA, and provide its logical characterisation. The complexity of the non-emptiness problem drops to NP. However, a number of existing formalisms and models studied in the literature can be captured already by weak ODTA. We also show that the definition of ODTA can be easily modified, to the case where the data values come from a tree-like partially ordered domain, such as strings.