J. Heintz
Abstract
An Algorithm is given which, as input, accepts a formula φ in prenex normal form, with prime formulas P=o, P≠o, for P ε Z [x1,...,x1], and some r ε N. It produces a quantifierfree formula ψ in disjunctive normal form (DNF) such that, in any algebraically closed field, φ ψ is true. The time required for a formula of length l with q quantifiers and r-q free variables is bounded by (c1·l) cr2 rq, for some constants c1, c2. If no ∀-quantifiers occur and the matrix of φ is in DNF, then the time is bounded by (c1·l)rcq2.
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