Solving Language Equations and Disequations with Applications to Disunification in Description Logics and Monadic Set Constraints

  • Franz Baader
  • Alexander Okhotin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7180)


We extend previous results on the complexity of solving language equations with one-sided concatenation and all Boolean operations to the case where also disequations (i.e., negated equations) may occur. To show that solvability of systems of equations and disequations is still in ExpTime, we introduce a new type of automata working on infinite trees, which we call looping automata with colors. As applications of these results, we show new complexity results for disunification in the description logic \(\mathcal{FL}_0\) and for monadic set constraints with negation. We believe that looping automata with colors may also turn out to be useful in other applications.


Description Logic Color Condition Acceptance Condition Language Expression Tree Automaton 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Franz Baader
    • 1
  • Alexander Okhotin
    • 2
  1. 1.Institute for Theoretical Computer ScienceTU DresdenGermany
  2. 2.Department of MathematicsUniversity of TurkuFinland

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