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SMT-Solving for the First-Order Theory of the Reals Abraham, Erika Loup, Ulrich SMT-solving first-order theory of the reals verification 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Erika Abraham and Ulrich Loup 2010 Is Part Of Dagstuhl Seminar Proceedings, Volume 9461, Algorithms and Applications for Next Generation SAT Solvers (2010) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/DagSemProc.09461.3 urn:nbn:de:0030-drops-25081 https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09461.3 eng https://creativecommons.org/licenses/by/4.0/legalcode