On the complexity of integer programming
Journal of the ACM (JACM)
A Web Odyssey: from Codd to XML
PODS '01 Proceedings of the twentieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
On XML integrity constraints in the presence of DTDs
Journal of the ACM (JACM)
Information and Computation
Query automata over finite trees
Theoretical Computer Science
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
Handbook of automated reasoning
Handbook of automated reasoning
Typechecking for XML transformers
Journal of Computer and System Sciences - Special issue on PODS 2000
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)
ACM Transactions on Database Systems (TODS) - Special Issue: SIGMOD/PODS 2004
A system for the static analysis of XPath
ACM Transactions on Information Systems (TOIS)
Alternation-free modal mu-calculus for data trees
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
Simple off the shelf abstractions for XML schema
ACM SIGMOD Record
XML data exchange: Consistency and query answering
Journal of the ACM (JACM)
On the Complexity of Verifying Consistency of XML Specifications
SIAM Journal on Computing
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)
Two-variable logic on data trees and XML reasoning
Journal of the ACM (JACM)
Boolean satisfiability from theoretical hardness to practical success
Communications of the ACM - A Blind Person's Interaction with Technology
Satisfiability of downward XPath with data equality tests
Proceedings of the twenty-eighth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
An Automata-Theoretic Approach to Regular XPath
DBPL '09 Proceedings of the 12th International Symposium on Database Programming Languages
Journal of Computer and System Sciences
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
Tree automata over infinite alphabets
Pillars of computer science
Parikh Images of Grammars: Complexity and Applications
LICS '10 Proceedings of the 2010 25th Annual IEEE Symposium on Logic in Computer Science
Efficient reasoning about data trees via integer linear programming
Proceedings of the 14th International Conference on Database Theory
Two-variable logic on data words
ACM Transactions on Computational Logic (TOCL)
On the complexity of equational horn clauses
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
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)
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Data trees provide a standard abstraction of XML documents with data values: they are trees whose nodes, in addition to the usual labels, can carry labels from an infinite alphabet (data). Therefore, one is interested in decidable formalisms for reasoning about data trees. While some are known—such as the two-variable logic—they tend to be of very high complexity, and most decidability proofs are highly nontrivial. We are therefore interested in reasonable complexity formalisms as well as better techniques for proving decidability. Here we show that many decidable formalisms for data trees are subsumed—fully or partially—by the power of tree automata together with set constraints and linear constraints on cardinalities of various sets of data values. All these constraints can be translated into instances of integer linear programming, giving us an NP upper bound on the complexity of the reasoning tasks. We prove that this bound, as well as the key encoding technique, remain very robust, and allow the addition of features such as counting of paths and patterns, and even a concise encoding of constraints, without increasing the complexity. The NP bound is tight, as we also show that the satisfiability of a single set constraint is already NP-hard. We then relate our results to several reasoning tasks over XML documents, such as satisfiability of schemas and data dependencies and satisfiability of the two-variable logic. As a final contribution, we describe experimental results based on the implementation of some reasoning tasks using the SMT solver Z3.