On the complexity of tree pattern containment with arithmetic comparisons

In this paper we investigate the complexity of query containment problem for tree patterns (which express a fragment of XPath) with arbitrary arithmetic comparisons. We assume that attributes take values from a totally ordered domain and allow constraints that involve arithmetic comparisons. We show that the containment problem is Π 2 P -complete in the general case, but remains co-NP complete for tree patterns with left semi-interval (, ⩾, =) attribute constraints. ► Query containment for tree patterns with arithmetic comparisons is studied. ► Query containment is Π 2 P -complete in the general case. ► For left (or right) semi-interval constraints, query containment is NP-complete.