# 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
3 Citations
Computing Exact Solutions of Consensus Halving and the Borsuk-Ulam Theorem
• Computer Science, Mathematics
• ICALP
• 2019
A new complexity class BU is defined, which captures all problems that can be reduced to solving an instance of the Borsuk-Ulam problem exactly, and it is shown that FIXP $\subseteq$ BU $\sub seteq$ TFETR and that LinearBU $=$ PPA, where LinearBU is the subclass of BU in which the BORSuk- Ulam instance is specified by a linear arithmetic circuit. Expand
Lipschitz Continuity and Approximate Equilibria
• Mathematics, Computer Science
• Algorithmica
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The key insight is that Lipschitz continuity of the payoff function allows us to provide algorithms for finding approximate equilibria in games with continuous action spaces and non-linear payoff functions. Expand
Algorithms and complexity of problems arising from strategic settings
This thesis deals with an evolutionary setting where it is shown that for a wide range of symmetric bimatrix games, deciding ESS existence is intractable, and presents a general framework for constructing approximation schemes for problems that can be written as an Existential Theory of the Reals formula with variables constrained in a bounded convex set. Expand

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