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A Nonlinear Real Arithmetic Fragment

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 8559)

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 and discuss applicability.

Keywords

  • Inference Rule
  • Decision Procedure
  • Real Eigenvalue
  • Input Formula
  • Cylindrical Algebraic Decomposition

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Supported in part by DARPA under contract FA8750-12-C-0284 and by the NSF grant SHF:CSR-1017483. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the funding agencies.

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Tiwari, A., Lincoln, P. (2014). A Nonlinear Real Arithmetic Fragment. In: Biere, A., Bloem, R. (eds) Computer Aided Verification. CAV 2014. Lecture Notes in Computer Science, vol 8559. Springer, Cham. https://doi.org/10.1007/978-3-319-08867-9_48

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  • DOI: https://doi.org/10.1007/978-3-319-08867-9_48

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08866-2

  • Online ISBN: 978-3-319-08867-9

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