Query Containment for Highly Expressive Datalog Fragments

The containment problem of Datalog queries is well knownto be undecidable. There are, however, several Datalog frag-ments for which containment is known to be decidable, mostnotably monadic Datalog and several “regular” query lan-guages on graphs. Monadically Defined Queries (MQs) havebeen introduced recently as a joint generalization of thesequery languages.In this paper, we study a wide range of Datalog frag-ments with decidable query containment and determine ex-act complexity results for this problem. We generalize MQsto (Frontier-)Guarded Queries (GQs), and show that the con-tainment problem is 3ExpTime-complete in either case, evenif we allow arbitrary Datalog in the sub-query. If we focuson graph query languages, i.e., fragments of linear Datalog,then this complexity is reduced to 2ExpSpace. We also con-sider nested queries, which gain further expressivity by us-ing predicates that are defined by inner queries. We showthat nesting leads to an exponentially increasing hierarchyfor the complexity of query containment, both in the linearand in the general case. Our results settle open problems for(nested) MQs, and they paint a comprehensive picture of thestate of the art in Datalog query containment.