  Dynamic complexity is concerned with updating the output of a problem when
the input is slightly changed. We study the dynamic complexity of two-player
parity games over graphs of bounded tree-width, where updates may add or delete
edges, or change the owner or color of states. We show that this problem is in
DynFO (with LOGSPACE precomputation); this is achieved by a reduction to a
Dyck-path problem on an acyclic automaton.
