Automata Can Show PSPACE Results for Description Logics

Franz BaaderFranz Baader, Jan HladikJan Hladik, Rafael PeñalozaRafael Peñaloza

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Franz Baader, Jan Hladik, Rafael Peñaloza
Automata Can Show PSPACE Results for Description Logics
Information and Computation, Special Issue: First International Conference on Language and Automata Theory and Applications (LATA'07), 206(9--10):1045-1056, 2008

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KurzfassungAbstract
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 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 with respect to acyclic terminologies in the DL SI, which extends the basic DL ALC with transitive and inverse roles.
Forschungsgruppe:Research Group: AutomatentheorieAutomata Theory

@article{ BaaHlaPen-IC-08,
  author = {Franz {Baader} and Jan {Hladik} and Rafael {Pe{\~n}aloza}},
  journal = {Information and Computation, Special Issue: First International Conference on Language and Automata Theory and Applications ({LATA'07})},
  number = {9--10},
  pages = {1045--1056},
  title = {Automata Can Show {PSPACE} Results for Description Logics},
  volume = {206},
  year = {2008},
}