SMT-Solving for the First-Order Theory of the Reals

Authors Erika Abraham, Ulrich Loup

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Erika Abraham
Ulrich Loup

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Erika Abraham and Ulrich Loup. SMT-Solving for the First-Order Theory of the Reals. In Algorithms and Applications for Next Generation SAT Solvers. Dagstuhl Seminar Proceedings, Volume 9461, pp. 1-7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


SAT-solving is a highly actual research area with increasing success and plenty of industrial applications. SMT-solving, extending SAT with theories, has its main focus on linear real constrains. However, there are only few solvers going further to more expressive but still decidable logics like the first-order theory of the reals with addition and multiplication. The main requests on theory solvers that must be fulfilled for their efficient embedding into an SMT solver are (a) incrementality, (b) the efficient computation of minimal infeasible subsets, and (c) the support of backtracking. For the first-order theory of the reals we are not aware of any solver offering those functionalities. In this work we address the possibilities to extend existing theory solving algorithms to come up with a theory solver suited for SMT.
  • SMT-solving
  • first-order theory of the reals
  • verification


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