Abstract
We present a new procedure for testing satisfiability (over the reals) of a conjunction of polynomial equations. There are three possible return values for our procedure: it either returns a model for the input formula, or it says that the input is unsatisfiable, or it fails because the applicability condition for the procedure, called the eigen-condition, is violated. For the class of constraints where the eigen-condition holds, our procedure is a decision procedure. We describe satisfiability-preserving transformations that can potentially convert problems into a form where eigen-condition holds. We experimentally evaluate the procedure on constraints generated by template-based verification and synthesis procedures.
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Acknowledgments
This work was sponsored, in part, by Defense Advanced Research Projects Agency (DARPA) and Air Force Research Laboratory (AFRL), under contract FA8750-12-C-0284, and the National Science Foundation under Grant CNS-1423298. The views, opinions, and/or findings contained in this report are those of the authors and should not be interpreted as representing the official views or policies, either expressed or implied, of the funding agencies.
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Tiwari, A., Lincoln, P. A search-based procedure for nonlinear real arithmetic. Form Methods Syst Des 48, 257–273 (2016). https://doi.org/10.1007/s10703-016-0245-8
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DOI: https://doi.org/10.1007/s10703-016-0245-8