Log depth circuits for division and related problems
SIAM Journal on Computing
On threshold circuits and polynomial computation
SIAM Journal on Computing
The complexity of iterated multiplication
Information and Computation
Incremental and decremental evaluation of transitive closure by first-order queries
Information and Computation
Dyn-FO: a parallel, dynamic complexity class
Journal of Computer and System Sciences - Special issue on principles of database systems
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
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
Proceedings of the 15th International Conference on Database Theory
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This paper presents a fully dynamic algorithm for maintaining the transitive closure of a directed graph. All updates and queries can be computed by constant depth threshold circuits of polynomial size (TC0 circuits). This places transitive closure in the dynamic complexity class DynTC0, and implies that transitive closure can be maintained in databases using updates written in a first order query language plus counting operators, while keeping the size of the database polynomial in the size of the graph.