Dynamic Complexity under Definable Changes

Dynamic Complexity under Definable Changes

This paper studies dynamic complexity under definable change operations in the DynFO framework by Patnaik and Immerman. It is shown that for changes definable by parameter-free firstorder formulas, all (uniform) AC1 queries can be maintained by first-order dynamic programs. Furthermore, many maintenance results for single-tuple changes are extended to more powerful change operations: (1) The re...

Dynamic Preference Aggregation under Preference Changes

We consider the issue of update in settings for preference aggregation under preference changes. While the traditional problem formulation of preference aggregation assumes a fixed set of preference orders and a fixed set of domain elements we investigate how an aggregated preference order has to be updated when the input orders are dynamic. Our analysis shows that for even for some simple aggr...

Martin Grohe Descriptive Complexity , Canonisation , and Definable Graph Structure Theory

On the Borel Complexity of MSO Definable Sets of Branches

An infinite binary word can be identified with a branch in the full binary tree. We consider sets of branches definable in monadic second-order logic over the tree, where we allow some extra monadic predicates on the nodes. We show that this class equals to the Boolean combinations of sets in the Borel class Σ 2 over the Cantor discontinuum. Note that the last coincides with the Borel complexit...

Counter Systems with Presburger-definable Reachability Sets : Decidability and Complexity

Model checking deals with the techniques of verifying whether a given formula in a suitably expressive logic is satisfied in a given abstract structure. The techniques as well as the cost for such task vary depending on the abstract formalism used to represent the model and the logic used to express the properties [CGP00]. For abstract formalism, it is worth to note that most of the practical s...