Approximating the Existential Theory of the Reals

@article{Deligkas2018ApproximatingTE,
  title={Approximating the Existential Theory of the Reals},
  author={Argyrios Deligkas and John Fearnley and Themistoklis Melissourgos and Paul G. Spirakis},
  journal={ArXiv},
  year={2018},
  volume={abs/1810.01393}
}
The existential theory of the reals (ETR) consists of existentially quantified boolean formulas over equalities and inequalities of real-valued polynomials. We propose the approximate existential theory of the reals (\(\epsilon \)-ETR), in which the constraints only need to be satisfied approximately. We first show that unconstrained \(\epsilon \)-ETR = ETR, and then study the \(\epsilon \)-ETR problem when the solution is constrained to lie in a given convex set. Our main theorem is a sampling… Expand
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