Finiteness Properties of Database Queries

We investigate the problem of checking whether the number of derivation trees of a Datalog program with duplicate semantics is nite or not. We show that given a safe stratiied query and an edb, it is possible to check, in polynomial time, whether the query has a nite number of derivation trees. However, it is undecidable to check whether a safe stratiied query has a nite number of derivation trees for every possible edb. We identify two classes of queries for which checking niteness over all edbs is decidable. We also deene duplicate semantics for Datalog (and thereby for the newly proposed variants of recursive SQL) queries with stratiied negation. Since evaluation involving counting of duplicates may not terminate in recursive SQL, this problem is of signiicant practical importance.