  We investigate the query evaluation problem for fixed queries over fully
dynamic databases, where tuples can be inserted or deleted. The task is to
design a dynamic algorithm that immediately reports the new result of a fixed
query after every database update. We consider queries in first-order logic
(FO) and its extension with modulo-counting quantifiers (FO+MOD), and show that
they can be efficiently evaluated under updates, provided that the dynamic
database does not exceed a certain degree bound.
  In particular, we construct a data structure that allows to answer a Boolean
FO+MOD query and to compute the size of the result of a non-Boolean query
within constant time after every database update. Furthermore, after every
update we are able to immediately enumerate the new query result with constant
delay between the output tuples. The time needed to build the data structure is
linear in the size of the database. Our results extend earlier work on the
evaluation of first-order queries on static databases of bounded degree and
rely on an effective Hanf normal form for FO+MOD recently obtained by Heimberg,
Kuske, and Schweikardt (LICS 2016).

Databases;Logic in Computer Science