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Superposition as a Decision Procedure for Timed Automata

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Abstract

The success of superposition-based theorem proving in first-order logic relies in particular on the fact that the superposition calculus can be turned into a decision procedure for various decidable fragments of first-order logic and has been successfully used to identify new decidable classes. In this paper, we extend this story to the hierarchic combination of linear arithmetic and first-order superposition. We show that decidability of reachability in timed automata can be obtained by instantiation of an abstract termination result for SUP(LA), the hierarchic combination of linear arithmetic and first-order superposition.

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Authors and Affiliations

  1. Max-Planck-Institut für Informatik, Saarbrücken, Germany

    Arnaud Fietzke & Christoph Weidenbach

  2. Computer Science, Saarland University, Saarbrücken, Germany

    Arnaud Fietzke & Christoph Weidenbach

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  1. Arnaud Fietzke
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Fietzke, A., Weidenbach, C. Superposition as a Decision Procedure for Timed Automata. Math.Comput.Sci. 6, 409–425 (2012). https://doi.org/10.1007/s11786-012-0134-5

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