∀∃ℝ-Completeness and Area-Universality

In the study of geometric problems, the complexity class \(\exists \mathbb {R}\) plays a crucial role since it exhibits a deep connection between purely geometric problems and real algebra. Sometimes \(\exists \mathbb {R}\) is referred to as the “real analogue” to the class NP. While NP is a class of computational problems that deals with existentially quantified boolean variables, \(\exists \mathbb {R}\) deals with existentially quantified real variables.

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