of quantifier alternation are thought of as being simpler, with the quantifier-free formulas as the simplest. A theory has quantifier elimination if for...

there is an algorithm that, given a quantifier-free formula defining a semialgebraic set, produces a quantifier-free formula for its projection. In fact...

form, that is, a string of quantifiers and bound variables followed by a quantifier-free formula. Quantifier elimination is a concept of simplification...

viewed as the theory of the methods to make quantifier elimination algorithmically effective. Quantifier elimination over the reals is another example, which...

quantifier elimination, every definable subset of an algebraically closed field is definable by a quantifier-free formula in one variable. Quantifier-free...

Presburger arithmetic Computing a Gröbner basis (in the worst case) Quantifier elimination on real closed fields takes at least double exponential time, and...

with each quantifier block limited to j variables. '<' is considered to be quantifier-free; here, bounded quantifiers are counted as quantifiers. PA(1, j)...

named after Alfred Tarski and Abraham Seidenberg. It implies that quantifier elimination is possible over the reals, that is that every formula constructed...

In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least...

Fourier–Motzkin elimination, also known as the FME method, is a mathematical algorithm for eliminating variables from a system of linear inequalities....

finite, then the Fraïssé limit of K {\displaystyle \mathbf {K} } has quantifier elimination. If the language of K {\displaystyle \mathbf {K} } is finite, and...

of quantifier elimination can be used to show that definable sets in particular theories cannot be too complicated. Tarski established quantifier elimination...

Tarski's quantifier elimination procedure for deciding statements in the first-order theory of the reals without the restriction to existential quantifiers. However...

induction Binary decision diagrams DPLL Higher-order unification Quantifier elimination Alt-Ergo Automath CVC E IsaPlanner LCF Mizar NuPRL Paradox Prover9...

Quantifier elimination. Current implementations of decision procedures for the theory of real closed fields are often based on quantifier elimination...

Kowloon, Hong Kong Queen Elizabeth Hospital, Adelaide, in Australia Quantifier elimination, a technique to simplify formulas Quadratic equation, an equation...

garbage collection by reference counting[G60] and of the method of quantifier elimination by cylindrical algebraic decomposition.[G75] He received his PhD...

double exponential complexity. CAD provides an effective version of quantifier elimination over the reals that has a much better computational complexity than...

topology. Equivalently, a d-constructible set is the set of solutions to a quantifier-free, or atomic, formula with parameters in K. Like the theory of algebraically...

with an acceptable complexity the Tarski–Seidenberg theorem on quantifier elimination over the real numbers. This theorem concerns the formulas of the...

are two quantifiers, one is the universal quantifier ∀ {\displaystyle \forall } (means "for all") and the other is the existential quantifier ∃ {\displaystyle...

theoretical study of the computational complexity of decidability and quantifier elimination in the first order theory of real numbers. The Sturm sequence and...

developed to make the argument rigorous. 1931 Alfred Tarski's real quantifier elimination. Improved and popularized by Abraham Seidenberg in 1954. (Both use...

any statement, either it or its negation is provable; have quantifier elimination; eliminate imaginaries; be finitely axiomatizable; be decidable: There...

(model theory) / Interpretable structure Pregeometry (model theory) Quantifier elimination Reduct Signature (logic) Skolem normal form Type (model theory)...

intervals and points. O-minimality can be regarded as a weak form of quantifier elimination. A structure M is o-minimal if and only if every formula with one...

PSPACE proof where no more than one universal quantifier is placed between each variable's use and the quantifier binding that variable. This was critical...

stability theory.[citation needed] In 1976, he proved a result on quantifier elimination for p-adic fields from which a theory of semi-algebraic and subanalytic...

full first order theory of the real numbers, are decidable using quantifier elimination. This is due to Alfred Tarski.) The first order theory of the natural...

Arbitrary precision Calculus Solvers Graph theory Number theory Quantifier elimination Boolean algebra Tensors Probability Control theory Group theory...