A Bibliography of Quantifier Elimination for Real Closed Fields

A basic collection of literature relatlng to algorithmic quantifier elimination for real closed fields is assembled.

[1]  George E. Collins,et al.  Quantifier Elimination for Real Closed Fields by Cylindrical Algebraic Decomposition: a synopsis , 1976, SIGS.

[2]  Jeanne Ferrante,et al.  A Decision Procedure for the First Order Theory of Real Addition with Order , 1975, SIAM J. Comput..

[3]  G. E. Collins,et al.  Quantifier Elimination for Real Closed Fields: A Guide to the Literature , 1983 .

[4]  H. R. Wüthrich,et al.  Ein Entscheidungsverfahren für die Theorie der reell- abgeschlossenen Körper , 1976, Komplexität von Entscheidungsproblemen 1976.

[5]  Leonard Berman,et al.  The Complexity of Logical Theories , 1980, Theor. Comput. Sci..

[6]  Dennis S. Arnon,et al.  Geometric Reasoning with Logic and Algebra , 1988, Artif. Intell..

[7]  Chandrajit L. Bajaj,et al.  Compliant motion planning with geometric models , 1987, SCG '87.

[8]  Dennis S. Arnon.  A Cluster-Based Cylindrical Algebraic Decomposition Algorithm , 1988, J. Symb. Comput..

[9]  C. Smoryński.  Skolem’s solution to a problem of frobenius , 1981 .

[10]  Scott McCallum,et al.  A Polynomial-Time Algorithm for the Topological Type of a Real Algebraic Curve , 1984, J. Symb. Comput..

[11]  Scott McCallum,et al.  An Improved Projection Operation for Cylindrical Algebraic Decomposition of Three-Dimensional Space , 1988, J. Symb. Comput..

[12]  A. Macintyre,et al.  Elimination of Quantifiers in Algebraic Structures , 1983 .

[13]  G. Wilson,et al.  Hilbert's sixteenth problem , 1978 .

[14]  Nachum Dershowitz,et al.  A Note on Simplification Orderings , 1979, Inf. Process. Lett..

[15]  Eduardo D. Sontag,et al.  Real Addition and the Polynomial Hierarchy , 1985, Inf. Process. Lett..

[16]  John H. Reif,et al.  The complexity of elementary algebra and geometry , 1984, STOC '84.

[17]  E. Becker.  On the real spectrum of a ring and its application to semialgebraic geometry , 1986 .

[18]  George E. Collins,et al.  Cylindrical Algebraic Decomposition I: The Basic Algorithm , 1984, SIAM J. Comput..

[19]  J. Davenport.  A "Piano Movers" Problem. , 1986 .

[20]  Sabine Stifter,et al.  Automated geometry theorem proving using Buchberger's algorithm , 1986, SYMSAC '86.

[21]  W. Böge,et al.  Quantifier Elimination for Real Closed Fields , 1985, AAECC.

[22]  Charles N. Delzell.  A continuous, constructive solution to Hilbert's 17th problem , 1984 .

[23]  Dennis S. Arnon,et al.  Topologically reliable display of algebraic curves , 1983, SIGGRAPH.

[24]  Dennis S. Arnon,et al.  A cellular decomposition algorithm for semi-algebraic sets , 1979, EUROSAM.

[25]  Tsit Yuen Lam,et al.  An introduction to real algebra , 1984 .

[26]  H. Whitney.  Elementary Structure of Real Algebraic Varieties , 1957 .

[27]  Micha Sharir,et al.  On Shortest Paths in Polyhedral Spaces , 1986, SIAM J. Comput..

[28]  Dima Grigoriev,et al.  Solving Systems of Polynomial Inequalities in Subexponential Time , 1988, J. Symb. Comput..

[29]  Bernard Chazelle,et al.  Fast Searching in a Real Algebraic Manifold with Applications to Geometric Complexity , 1985, TAPSOFT, Vol.1.

[30]  B. E. Meserve.  Decision Methods for Elementary Algebra , 1955 .

[31]  M. A. Dickmann,et al.  Applications of model theory to real algebraic geometry , 1985 .

[32]  James H. Davenport.  A :20piano movers' ' , 1986, SIGS.

[33]  Stefan Arnborg,et al.  Algebraic Decomposition of Regular Curves , 1988, J. Symb. Comput..

[34]  Volker Weispfenning,et al.  The Complexity of Linear Problems in Fields , 1988, Journal of symbolic computation.

[35]  Michel Coste,et al.  Thom's Lemma, the Coding of Real Algebraic Numbers and the Computation of the Topology of Semi-Algebraic Sets , 1988, J. Symb. Comput..

[36]  Joos Heintz,et al.  Corrigendum: Definability and Fast Quantifier Elimination in Algebraically Closed Fields , 1983, Theor. Comput. Sci..

[37]  D A Gudkov,et al.  THE TOPOLOGY OF REAL PROJECTIVE ALGEBRAIC VARIETIES , 1974 .

[38]  B. L. Waerden,et al.  Das Problem der dreizehn Kugeln , 1952 .

[39]  George E. Collins.  The Tarski decision procedure , 1956, ACM '56.

[40]  Jean-Jacques Risler.  Some Aspects of Complexity in Real Algebraic Geometry , 1988, J. Symb. Comput..

[41]  Gregory W. Brumfiel,et al.  Partially Ordered Rings and Semi-Algebraic Geometry , 1980 .

[42]  George E. Collins.  Factorization in Cylindrical Algebraic Decomposition , 1982, EUROCAM.

[43]  George E. Collins,et al.  Quantifier elimination for real closed fields by cylindrical algebraic decomposition , 1975 .

[44]  Chee-Keng Yap,et al.  Algebraic cell decomposition in NC , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[45]  Joos Heintz,et al.  An efficient quantifier elimination algorithm for algebraically closed fields of any characteristic , 1975, SIGS.

[46]  George E. Collins,et al.  An Adjacency Algorithm for Cylindrical Algebraic Decompositions of Three-Dimensional Space , 1988, J. Symb. Comput..

[47]  Daniel Lazard,et al.  Quantifier Elimination: Optimal Solution for Two Classical Examples , 1988, J. Symb. Comput..

[48]  A. Tarski.  What is Elementary Geometry , 1959 .

[49]  A. Seidenberg.  A NEW DECISION METHOD FOR ELEMENTARY ALGEBRA , 1954 .

[50]  A. Tarski.  A Decision Method for Elementary Algebra and Geometry , 2023 .

[51]  John F. Canny,et al.  A new algebraic method for robot motion planning and real geometry , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[52]  D. Grigor'ev.  Complexity of deciding Tarski algebra , 1988 .

[53]  Micha Sharir,et al.  A Survey of Motion Planning and Related Geometric Algorithms , 1988, Artificial Intelligence.

[54]  J. Schwartz,et al.  On the “piano movers” problem. II. General techniques for computing topological properties of real algebraic manifolds , 1983 .

[55]  George E. Collins,et al.  Cylindrical Algebraic Decomposition II: An Adjacency Algorithm for the Plane , 1984, SIAM J. Comput..

[56]  Paul J. Cohen,et al.  Decision procedures for real and p‐adic fields , 1969 .

[57]  Maurice Mignotte,et al.  On Mechanical Quantifier Elimination for Elementary Algebra and Geometry , 1988, J. Symb. Comput..

[58]  Scott McCallum,et al.  Cylindrical Algebraic Decomposition by Quantifier Elimination , 1982, EUROCAM.

[59]  David Prill.  On Approximations and Incidence in Cylindrical Algebraic Decompositions , 1986, SIAM J. Comput..

[60]  Deepak Kapur,et al.  A Refutational Approach to Geometry Theorem Proving , 1988, Artif. Intell..

[61]  D. Dubois.  A nullstellensatz for ordered fields , 1970 .

[62]  P. J. Kahn,et al.  Counting types of rigid frameworks , 1979 .

[63]  Deepak Kapur,et al.  Geometry theorem proving using Hilbert's Nullstellensatz , 1986, SYMSAC '86.

[64]  James H. Davenport,et al.  Real Quantifier Elimination is Doubly Exponential , 1988, J. Symb. Comput..