  A dynamic program, as introduced by Patnaik and Immerman (1994), maintains
the result of a fixed query for an input database which is subject to tuple
insertions and deletions. It can use an auxiliary database whose relations are
updated via first-order formulas upon modifications of the input database. This
paper studies static analysis problems for dynamic programs and investigates,
more specifically, the decidability of the following three questions. Is the
answer relation of a given dynamic program always empty? Does a program
actually maintain a query? Is the content of auxiliary relations independent of
the modification sequence that lead to an input database? In general, all these
problems can easily be seen to be undecidable for full first-order programs.
Therefore the paper aims at pinpointing the exact decidability borderline for
programs with restricted arity (of the input and/or auxiliary database) and
restricted quantification.
