Solving language equations and disequations with applications to disunification in description logics and monadic set constraints

Authors:
Franz Baader;Alexander Okhotin
Affiliations:
Institute for Theoretical Computer Science, TU Dresden, Germany;Department of Mathematics, University of Turku, Finland
Venue:
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Year:
2012

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Abstract

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 FL0 and for monadic set constraints with negation. We believe that looping automata with colors may also turn out to be useful in other applications.