Data Exchange with Arithmetic Comparisons∗

In this paper, the problem of data exchange in the presence of arithmetic comparisons is studied. For this purpose, tuple generating dependencies with arithmetic comparisons (tgd-AC) and arithmetic comparison generating dependencies (acgd) are introduced to capture the need to use arithmetic comparisons in source-totarget and in target constraints (both in their antecedent and in their consequent). Arithmetic comparisons are interpreted over densely totally ordered domains. A chase procedure called AC-chase is introduced to handle such constraints. AC-chase is a tree rather than a sequence and its depth is polynomial on the size of the source instance if the set of target constraints is the union of a set of target acgds with a weakly acyclic set of target tgd-ACs. It is shown that AC-chase computes a universal solution which can be used to compute certain answers for unions of conjunctive queries with arithmetic comparisons (UCQAC). The complexity of existence of a solution is shown to be in NP. The complexity of computing certain answers of UCQAC queries is shown to be coNP-complete. In order to identify polynomial cases, we introduce the succinct AC-chase which however does not always produce a solution. We identify cases where its result is a universal solution and we investigate the syntactic conditions of the query under which we can use the result of succinct AC-chase to compute the certain answers in polynomial time. We show that the latter is also feasible in cases where the result of succinct chase is not a universal solution.