Static Analysis for Logic-based Dynamic Programs

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.