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

Answering FO+MOD queries under updates on bounded degree databases