Dynamic Complexity of the Dyck Reachability
  Dynamic complexity is concerned with updating the output of a problem when the input is slightly changed. We study the dynamic complexity of Dyck reachability problems in directed and undirected graphs, where updates may add or delete edges. We show a strong dichotomy between such problems, based on the size of the Dyck alphabet. Some of them are P-complete (under a strong notion of reduction) while the others lie either in DynFO or in NL. 
Patricia Bouyer and Vincent Jug\'e
cs.CC