A faster PSPACE algorithm for deciding the existential theory of the reals

The decision problem for the existential theory of the reals is the problem of deciding if the set (x in R/sup n/; P(x) is nonempty, where P(x) is a predicate which is a Boolean function of atomic predicates either of which is a Boolean function of atomic predicates either of the form f/sub i/(x)>or=0 or f/sub j/(x)>, the f's being real polynomials. An algorithm is presented for deciding the existential theory of the reals that simultaneously achieves the best known time and space bounds. The time bound for the algorithm is slightly better than any previous bound.<>