摘要：This paper studies dynamic complexity under definable change operations in the DynFO framework by Patnaik and Immerman. It is shown that for changes definable by parameter-free first-order formulas, all (uniform) AC1 queries can be maintained by first-order dynamic programs. Furthermore, many maintenance results for single-tuple changes are extended to more powerful change operations: (1) The reachability query for undirected graphs is first-order maintainable under single tuple changes and first-order defined insertions, likewise the reachability query for directed acyclic graphs under quantifier-free insertions. (2) Context-free languages are first-order maintainable under \EFO-defined changes. These results are complemented by several inexpressibility results, for example, that the reachability query cannot be maintained by quantifier-free programs under definable, quantifier-free deletions.
