Abstract
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.
Reproduced from Automata Theory and Formal Languages (Lecture Notes in Computer Science, vol. 33), edited by H. Brakhage, with permission of Springer-Verlag, with corrections by the author.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer-Verlag/Wien
About this paper
Cite this paper
Collins, G.E. (1998). Quantifier Elimination for Real Closed Fields by Cylindrical Algebraic Decomposition. In: Caviness, B.F., Johnson, J.R. (eds) Quantifier Elimination and Cylindrical Algebraic Decomposition. Texts and Monographs in Symbolic Computation. Springer, Vienna. https://doi.org/10.1007/978-3-7091-9459-1_4
Download citation
DOI: https://doi.org/10.1007/978-3-7091-9459-1_4
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82794-9
Online ISBN: 978-3-7091-9459-1
eBook Packages: Springer Book Archive