Languages that capture complexity classes
SIAM Journal on Computing
Maintaining views incrementally
SIGMOD '93 Proceedings of the 1993 ACM SIGMOD international conference on Management of data
Computing with first-order logic
Selected papers of the 23rd annual ACM symposium on Theory of computing
On a monadic NP vs monadic co-NP
Information and Computation
Principles of programming with complex objects and collection types
ICDT '92 Selected papers of the fourth international conference on Database theory
Dyn-FO: a parallel, dynamic complexity class
Journal of Computer and System Sciences - Special issue on principles of database systems
Query languages for bags and aggregate functions
Journal of Computer and System Sciences - Special issue on principles of database systems
Dynamic tree isomorphism via first-order updates to a relational database
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Journal of Computer and System Sciences - Fourteenth ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems
Foundations of Databases: The Logical Level
Foundations of Databases: The Logical Level
Local Properties of Query Languages
ICDT '97 Proceedings of the 6th International Conference on Database Theory
On Impossibility of Decremental Recomputation of Recursive Queries in Relational Calculus and SQL
DBLP-5 Proceedings of the Fifth International Workshop on Database Programming Languages
Incremental Recomputation of Recursive Queries with Nested Sets and Aggregate Functions
DBLP-6 Proceedings of the 6th International Workshop on Database Programming Languages
On Counting Logics and Local Properties
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
Logics with Aggregate Operators
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Dynamic complexity theory revisited
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Efficient incremental validation of XML documents after composite updates
XSym'06 Proceedings of the 4th international conference on Database and XML Technologies
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We consider IES(SQL), the incremental evaluation system over an SQL-like language with grouping, arithmetics, and aggregation. We show that every second order query is in IES(SQL) and that there are PSPACE-complete queries in IES(SQL). We further show that every PSPACE query is in IES(SQL) augmented with a deterministic transitive closure operator. Lastly, we consider ordered databases and provide a complete analysis of a hierarchy on IES(SQL) defined with respect to arity-bounded auxiliary relations.