How can the result of a query be updated after changing a database? This is a fundamental
task for database management systems which ideally takes previously computed …

In the setting of DynFO, dynamic programs update the stored result of a query whenever the
underlying data changes. This update is expressed in terms of first-order logic. We introduce …

We initiate the study of graph algorithms in the streaming setting on massive distributed and
parallel systems inspired by practical data processing systems. The objective is to design …

Recently it was shown that the transitive closure of a directed graph can be updated using
first-order formulas after insertions and deletions of single edges in the dynamic descriptive …

In the setting of dynamic complexity, the goal of a dynamic program is to maintain the result
of a fixed query for an input database that is subject to changes, possibly using additional …

In 2015, it was shown that reachability for arbitrary directed graphs can be updated by first-
order formulas after inserting or deleting single edges. Later, in 2018, this was extended for …

Which dynamic queries can be maintained efficiently? For constant-size changes, it is
known that constant-depth circuits or, equivalently, first-order updates suffice for maintaining …

Whether a changing string is member of a certain regular language can be maintained in the
DynFO framework of Patnaik and Immerman: after changing the symbol at one position of …

Let $ G $ be a finite group given as input by its multiplication table. For a subset $ S $ of $ G
$ and an element $ g\in G $ the Cayley Group Membership Problem (denoted CGM) is to …

Reachability, distance, and matching are some of the most fundamental graph problems that
have been of particular interest in dynamic complexity theory in recent years [DKMSZ18 …