# SI! Automata Can Show PSPACE Results for Description Logics

From International Center for Computational Logic

# SI! Automata Can Show PSPACE Results for Description Logics

##### Franz BaaderFranz Baader, J. HladikJ. Hladik, R. PeñalozaR. Peñaloza

Franz Baader, J. Hladik, R. Peñaloza

In C. Martin-Vide, eds.,

**SI! Automata Can Show PSPACE Results for Description Logics**In C. Martin-Vide, eds.,

*Proceedings of the First International Conference on Language and Automata Theory and Applications (LATA'07)*, 2007**Kurzfassung****Abstract**

In Description Logics (DLs), 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 PSPACE-complete logics, it is often very hard to design optimal tableau-based algorithms for EXPTIME-complete DLs. In contrast, the automata-based approach is usually well-suited to prove EXPTIME upper-bounds, but its direct application will usually also yield an EXPTIME-algorithm for a PSPACE-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 PSPACE-algorithm. We illustrate the usefulness of this approach by proving a new PSPACE upper-bound for satisfiability of concepts w.r.t. acyclic terminologies in the DL SI, which extends the basic DL ALC with transitive and inverse roles.**Forschungsgruppe:****Research Group:**AutomatentheorieAutomata Theory

```
@inproceedings{ BaaHlaPen-LATA-07,
author = {F. {Baader} and J. {Hladik} and R. {Pe{\~n}aloza}},
booktitle = {Proceedings of the First International Conference on Language and Automata Theory and Applications ({LATA'07})},
editor = {C. {Martin-Vide}},
title = {{SI}! Automata Can Show {PSPACE} Results for Description Logics},
year = {2007},
}
```