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

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Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7180))

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 \(\mathcal{FL}_0\) and for monadic set constraints with negation. We believe that looping automata with colors may also turn out to be useful in other applications.

Supported by DFG (BA 1122/14-1) and the Academy of Finland (grant 134860).

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Author information

Authors and Affiliations

  1. Institute for Theoretical Computer Science, TU Dresden, Germany

    Franz Baader

  2. Department of Mathematics, University of Turku, Finland

    Alexander Okhotin

Authors
  1. Franz Baader
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  2. Alexander Okhotin
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Editor information

Editors and Affiliations

  1. Microsoft Research, One Microsoft Way, 98052-6399, Redmond, WA, USA

    Nikolaj Bjørner

  2. School of computer Science, University of Manchester, Kilburn Building, Oxford Road, MP13 9PL, Manchester, UK

    Andrei Voronkov

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Baader, F., Okhotin, A. (2012). Solving Language Equations and Disequations with Applications to Disunification in Description Logics and Monadic Set Constraints. In: Bjørner, N., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2012. Lecture Notes in Computer Science, vol 7180. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28717-6_11

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  • DOI: https://doi.org/10.1007/978-3-642-28717-6_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28716-9

  • Online ISBN: 978-3-642-28717-6

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