A Nonlinear Real Arithmetic Fragment

Abstract

We present a new procedure for testing satisability (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 satisability-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.