Processing first-order queries under limited access patterns

We study the problem of answering queries over sources with limited access patterns. Given a first-order query Q, the problem is to decide whether there is an equivalent query which can be executed observing the access patterns restrictions. If so, we say that Q is feasible. We define feasible for first-order queries - previous definitions handled only some existential cases - and characterize the complexity of many first-order query classes. For each of them, we show that deciding feasibility is as hard as deciding containment. Since feasibility is undecidable in many cases and hard to decide in some others, we also define an approximation to it which can be computed in NP for any first-order query and in P for unions of conjunctive queries with negation. Finally, we outline a practical overall strategy for processing first-order queries under limited access patterns.