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The Computer Journal 1993 36(5):427-431; doi:10.1093/comjnl/36.5.427
© 1993 by British Computer Society
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On the Theoretical and Practical Complexity of the Existential Theory of Reals

J. Heintz1 *, M.-F. Roy2 § and P. Solernò3 ¶

1 Universitad de Cantabria, Santander, Spain, 2 Inst. Argentino de Matematica, CONICET, Viamonte 1636, (1055) Buenos Aires, Argentina, 3 IRMAR (URA CNRS 305), Universite de Rennes, 35042 Rennes cedex, France

Recently several theoretical single exponential time algorithms (in the number of variables) have been proposed for deciding the existential theory of reals. These algorithms have from a complexity analysis point of view a much better behaviour than CAD which was doubly exponential in the number of variables, but an efficient implementation based on these new ideas has never been performed yet. This paper is devote to the development of the following idea "it is possible to implement efficiently slight variants of single exponential methods well adapted to important particular cases of the decision problem". We explain the main ideas, propose more efficient versions of the methods and make concrete propositions for future experiments*.

Received January 1993. revised May 1993.

* Universitad de Cantabria, Santander, Spain

§ Inst. Argentino de Matemática, CONICET, Viamonte 1636, (1055) Buenos Aires, Argentina

IRMAR (URA CNRS 305), Université de Rennes, 35042 Rennes cedex, France


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