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Don’t care words with an application to the automata-based approach for real addition

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Abstract

Automata have proved to be a useful tool in infinite-state model checking, since they can represent infinite sets of integers and reals. However, analogous to the use of binary decision diagrams (bdds) to represent finite sets, the sizes of the automata are an obstacle in the automata-based set representation. In this article, we generalize the notion of “don’t cares” for bdds to word languages as a means to reduce the automata sizes. We show that the minimal weak deterministic Büchi automaton (wdba) with respect to a given don’t care set, under certain restrictions, is uniquely determined and can be efficiently constructed. We apply don’t cares to improve the efficiency of a decision procedure for the first-order logic over the mixed linear arithmetic over the integers and the reals based on wdbas.

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Authors and Affiliations

  1. Department of Computer Science, Albert-Ludwigs-Universität Freiburg, Georges-Köhler-Allee 051, 79110, Freiburg, Germany

    Jochen Eisinger

  2. Computer Science Department, ETH Zurich, Haldeneggsteig 4, IFW C 47.2, 8092, Zurich, Switzerland

    Felix Klaedtke

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  1. Jochen Eisinger
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Correspondence to Felix Klaedtke.

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Eisinger, J., Klaedtke, F. Don’t care words with an application to the automata-based approach for real addition. Form Methods Syst Des 33, 85–115 (2008). https://doi.org/10.1007/s10703-008-0057-6

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