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We study the problem of consistent query answering under primary keyviolations. In this setting, the relations in a database violate the keyconstraints and we are interested in maximal subsets of the database thatsatisfy the constraints, which we call repairs. For a boolean query Q, theproblem CERTAINTY(Q) asks whether every such repair satisfies the query or not;the problem is known to be always in coNP for conjunctive queries. However,there are queries for which it can be solved in polynomial time. It has beenconjectured that there exists a dichotomy on the complexity of CERTAINTY(Q) forconjunctive queries: it is either in PTIME or coNP-complete. In this paper, weprove that the conjecture is indeed true for the case of conjunctive querieswithout self-joins, where each atom has as a key either a single attribute(simple key) or all attributes of the atom.

A Dichotomy on the Complexity of Consistent Query Answering for Atoms with Simple Keys