Bag Equivalence of Bounded Symmetry-Degree Conjunctive Queries with Inequalities

We consider the problem of checking equivalence of conjunctive queries with inequalities under bag (multiset) semantics. The problem is known to be decidable in pspace and as hard as graph isomorphism, but its exact complexity remains open. We introduce a natural restriction based on what we call the symmetry degree of queries, and show that when the symmetry degree is bounded by a fixed polynomial in the size of the query, the equivalence problem is in Πp 2 . We also show that for asymmetric queries (those of symmetry degree 1), checking bag-equivalence is polynomial-time Turing equivalent to the graph automorphism problem. These results can be interpreted as first steps in a more general program of finding “islands of tractability” for testing equivalence of conjunctive queries with inequalities under bag (rather than set) semantics.