  The present paper investigates the dynamic complexity of document spanners, a
formal framework for information extraction introduced by Fagin, Kimelfeld,
Reiss, and Vansummeren (JACM 2015). We first look at the class of regular
spanners and prove that any regular spanner can be maintained in the dynamic
complexity class DynPROP. This result follows from work done previously on the
dynamic complexity of formal languages by Gelade, Marquardt, and Schwentick
(TOCL 2012).
  To investigate core spanners we use SpLog, a concatenation logic that exactly
captures core spanners. We show that the dynamic complexity class DynCQ, is
more expressive than SpLog and therefore can maintain any core spanner. This
result is then extended to show that DynFO can maintain any generalized core
spanner and that DynFO is at least as powerful as SpLog with negation.
