Automata can show PSpace results for description logics

In the area of Description Logic (DL), both tableau-based and automata-based algorithms are frequently used to show decidability and complexity results for basic inference problems such as satisfiability of concepts. Whereas tableau-based algorithms usually yield worst-case optimal algorithms in the case of PS-complete logics, it is often very hard to design optimal tableau-based algorithms for ET-complete DLs. In contrast, the automata-based approach is usually well-suited to prove ET upper-bounds, but its direct application will usually also yield an ET-algorithm for a PS-complete logic since the (tree) automaton constructed for a given concept is usually exponentially large. In the present paper, we formulate conditions under which an on-the-fly construction of such an exponentially large automaton can be used to obtain a PS-algorithm. We illustrate the usefulness of this approach by proving a new PS upper-bound for satisfiability of concepts with respect to acyclic terminologies in the DL , which extends the basic DL with transitive and inverse roles.