Quantifier Elimination for Real Closed Fields by Cylindrical Algebraic Decomposition

  • George E. Collins
Conference paper
Part of the Texts and Monographs in Symbolic Computation book series (TEXTSMONOGR)


Tarski in 1948, (Tarski 1951) published a quantifier elimination method for the elementary theory of real closed fields (which he had discovered in 1930). As noted by Tarski, any quantifier elimination method for this theory also provides a decision method, which enables one to decide whether any sentence of the theory is true or false. Since many important and difficult mathematical problems can be expressed in this theory, any computationally feasible quantifier elimination algorithm would be of utmost significance.


Real Root Atomic Formula Real Zero Real Polynomial Quantifier Elimination 
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Copyright information

© Springer-Verlag/Wien 1998

Authors and Affiliations

  • George E. Collins

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