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Recently, various natural algorithmic problems have been shown to be $\exists \mathbb{R}$-complete.
The design and analysis of computer algorithms
Alfred V. Aho, John E. Hopcroft, and Jeffrey D. Ullman · 1975
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Some algebraic and geometric computations in PSPACE
John Canny · 1988
Earlier work this paper cites.
The universality theorems on the classification problem of configuration varieties and convex polytopes varieties
Nicolai E Mnëv · 1988
Earlier work this paper cites.
Stretchability of pseudolines is NP-hard
Peter W. Shor · 1991
Earlier work this paper cites.
Complexity of some geometric and topological problems
Marcus Schaefer · 2009
Earlier work this paper cites.
Bounding the radii of balls meeting every connected component of semi-algebraic sets
Saugata Basu and Marie-Françoise Roy · 2010
Cited alongside, same era.
Complexity and real computation
Lenore Blum, Felipe Cucker, Michael Shub, and Steve Smale · 2012
Cited alongside, same era.
Realizability of graphs and linkages
Marcus Schaefer · 2013
Cited alongside, same era.
Intersection graphs of segments and ∃ ℝ \exists\mathbb{R}
Jiří Matoušek · 2014
Cited alongside, same era.
∀ ∃ ℝ \forall\exists\mathbb{R} -completeness and area-universality
Michael G. Dobbins, Linda Kleist, Tillmann Miltzow, and Paweł Rza̧żewski · 2017
Cited alongside, same era.
On a general method of describing plane curves of the n th n^{\text{th}} degree by linkwork
A. B. Kempe
Cited in the paper.
Fixed points, Nash equilibria, and the existential theory of the reals
Marcus Schaefer and Daniel Štefankovič · 2017
Later among the works it cites.
The art gallery problem is ∃ ℝ \exists\mathbb{R} -complete
Mikkel Abrahamsen, Anna Adamaszek, and Tillmann Miltzow · 2018
Later among the works it cites.
The complexity of drawing a graph in a polygonal region
Anna Lubiw, Tillmann Miltzow, and Debajyoti Mondal · 2018
Later among the works it cites.
A universality theorem for nested polytopes
Michael Gene Dobbins, Andreas Holmsen, and Tillmann Miltzow · 2019
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