Logical aspects in the study of tree languages
Proc. of the conference on Ninth colloquium on trees in algebra and programming
Computational learning theory: an introduction
Computational learning theory: an introduction
An algebraic characterization of frontier testable tree languages
ICALP Selected papers of the twentieth international colloquium on Automata, languages and programming
Languages, automata, and logic
Handbook of formal languages, vol. 3
Complexity of nonrecursive logic programs with complex values
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Finite queries do not have effective syntax
Information and Computation
Expressive and efficient pattern languages for tree-structured data (extended abstract)
PODS '00 Proceedings of the nineteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
PODS '00 Proceedings of the nineteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Ordering constraints over feature trees expressed in second-order monadic logic
Information and Computation - Special issue on RTA-98
Relational queries over interpreted structures
Journal of the ACM (JACM)
The first-order theory of subtyping constraints
POPL '02 Proceedings of the 29th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Introduction to Circuit Complexity: A Uniform Approach
Introduction to Circuit Complexity: A Uniform Approach
Foundations of Databases: The Logical Level
Foundations of Databases: The Logical Level
Query automata over finite trees
Theoretical Computer Science
Ordering Constraints over Feature Trees
Constraints
Set Constraints: Results, Applications, and Future Directions
PPCP '94 Proceedings of the Second International Workshop on Principles and Practice of Constraint Programming
Axiomatizing the Equational Theory of Regular Tree Languages (Extended Anstract)
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Relating Hierarchies of Word and Tree Automata
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
The Oz Programming Model (Extended Abstract)
Euro-Par '95 Proceedings of the First International Euro-Par Conference on Parallel Processing
MONA 1.x: New Techniques for WS1S and WS2S
CAV '98 Proceedings of the 10th International Conference on Computer Aided Verification
Regular Tree Languages Without Unary Symbols are Star-Free
FCT '93 Proceedings of the 9th International Symposium on Fundamentals of Computation Theory
Automatic Presentations of Structures
LCC '94 Selected Papers from the International Workshop on Logical and Computational Complexity
Typechecking for Semistructured Data
DBPL '01 Revised Papers from the 8th International Workshop on Database Programming Languages
Relating word and tree automata
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
Definable relations and first-order query languages over strings
Journal of the ACM (JACM)
Feature logic with weak subsumption constraints
ACL '91 Proceedings of the 29th annual meeting on Association for Computational Linguistics
TQL: a query language for semistructured data based on the ambient logic
Mathematical Structures in Computer Science
Conditional XPath, the first order complete XPath dialect
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
The complexity of XPath query evaluation and XML typing
Journal of the ACM (JACM)
Recurrent Reachability Analysis in Regular Model Checking
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Hyperset Approach to Semi-structured Databases
BNCOD 26 Proceedings of the 26th British National Conference on Databases: Dataspace: The Final Frontier
Queries on Xml streams with bounded delay and concurrency
Information and Computation
Weak Kripke structures and LTL
CONCUR'11 Proceedings of the 22nd international conference on Concurrency theory
Regular languages of nested words: fixed points, automata, and synchronization
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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We study relations on trees defined by first-order constraints over a vocabulary that includes the tree extension relation T ≺ T′ (holding if and only if every branch of T extends to a branch of T′), unary node-tests, and a binary relation checking whether the domains of two trees are equal. We consider both ranked and unranked trees. These are trees with and without a restriction on the number of children of nodes. We adopt the model-theoretic approach to tree relations and study relations definable over the structure consisting of the set of all trees and the aforementioned predicates. We relate definability of sets and relations of trees to computability by tree automata. We show that some natural restrictions correspond to familiar logics in the more classical setting where every tree is a structure over a fixed vocabulary, and to logics studied in the context of XML pattern languages. We then look at relational calculi over collections of trees, and obtain quantifier-restriction results that give us bounds on the expressive power and complexity. As unrestricted relational calculi can express problems that are complete for each level of the polynomial hierarchy, we look at their restrictions, corresponding to the restricted logics over the family of all unranked trees, and find several calculi with low (NC1) data complexity which still express properties important for database and document applications. We also give normal forms for safe queries in the calculus.