Solving systems of polynomial inequalities in subexponential time
Journal of Symbolic Computation
Complexity of deciding Tarski algebra
Journal of Symbolic Computation
The complexity of deciding consistency of systems of polynomials in exponent inequalities
Journal of Symbolic Computation
Complexity lower bounds for computation trees with elementary transcendental function gates
Theoretical Computer Science - Special issue on complexity theory and the theory of algorithms as developed in the CIS
On the combinatorial and algebraic complexity of quantifier elimination
Journal of the ACM (JACM)
Complexity and real computation
Complexity and real computation
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Ein Entscheidungsverfahren für die Theorie der reell- abgeschlossenen Körper
Komplexität von Entscheidungsproblemen, Ein Seminar
Deciding polynomial-exponential problems
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Deciding polynomial-transcendental problems
Journal of Symbolic Computation
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Tarski-Seidenberg principle plays a key role in many applications and algorithm of computer algebra. Moreover it is constructive, and some very efficient quantifier elimination algorithms appeared recently. However, Tarski-Seidenberg principle is wrong for first-order theories involving some real analytic functions (e.g. an exponential function). In this case a weaker statement is sometimes true, a possibility to eliminate one sort of quantifiers (either ∀ or ∃). We construct a new algorithm for a cylindrical cell decomposition of a closed cube In ⊄ Rn compatible with a semianalytic subset S ⊄ In, defined by Pfaffian functions. In particular the algorithm is able to eliminate one sort of quantifiers from a first-order formula. The complexity bound of the algorithm is doubly exponential in n2.