Dynamic Complexity of Planar 3-Connected Graph Isomorphism

Dynamic Complexity (as introduced by Patnaik and Immerman [14]) tries to express how hard it is to update the solution to a problem when the input is changed slightly. It considers the changes required to some stored data structure (possibly a massive database) as small quantities of data (or a tuple) are inserted or deleted from the database (or a structure over some vocabulary). The main difference from previous notions of dynamic complexity is that instead of treating the update quantitatively by finding the the time/space trade-offs, it tries to consider the update qualitatively, by finding the complexity class in which the update can be expressed (or made). In this setting, DynFO, or Dynamic First-Order, is one of the smallest and the most natural complexity class (since SQL queries can be expressed in First-Order Logic), and contains those problems whose solutions (or the stored data structure from which the solution can be found) can be updated in First-Order Logic when the data structure undergoes small changes.