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George Collins discovery of Cylindrical Algebraic Decomposition
(CAD) as a method for Quantifier Elimination (QE) for the
elementary theory of real closed fields brought a major
breakthrough in automating mathematics with recent important
applications in high-tech areas (e.g. robot motion), also
stimulating fundamental research in computer algebra over the past
three decades. This volume is a state-of-the art collection of
important papers on CAD and QE and on the related area of
algorithmic aspects of real geometry. In addition to original
contributions by S. Basu et al., L. Gonzalez-Vega et al., G. Hagel,
H. Hong and J.R. Sendra, J.R. Johnson, S. McCallum, D. Richardson,
and V. Weispfenning and a survey by G.E. Collins outlining the
twenty-year progress in CAD-based QE it brings together seminal
publications from the area: A. Tarski: A Decision Method for
Elementary Algebra and Geometry G.E. Collins: Quantifier
Elimination for Real Closed Fields by Cylindrical Algebraic
Decomposition M.J. Fischer and M.O. Rabin: Super-Exponential
Complexity of Presburger Arithmetic D.S. Arnon et al.: Cylindrical
Algebraic Decomposition I: The Basic Algorithm; II: An Adjacency
Algorithm for the Plane H. Hong: An Improvement of the Projection
Operator in Cyclindrical Algebraic Decomposition G.E. Collins and
H. Hong: Partial Cylindrical Algebraic Decomposition for Quantifier
Elimination H. Hong: Simple Solution Formula Construction in
Cylindrical Algebraic Decomposition Based Quantifier Elimination J.
Renegar: Recent Progress on the Complexity of the Decision Problem
for the Reals
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