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Local quantifier elimination

Andreas Dolzmann, Volker Weispfenning

Open publisher page 6 citations

Abstract

We introduce local quantifier elimination as a new variant of real quantifier elimination. Given a first-order formula and a real point we compute a quantifier-free formula which is not only for the given point equivalent to the input formula but also for all points in a semi-algebraic set containing the specified point. The description of this semi-algebraic set is explicitly computed in the form of a conjunction of atomic formulas. Local quantifier elimination is in its application area superior to both regular and generic quantifier elimination due to faster running times and shorter results.

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What this paper is about

We introduce local quantifier elimination as a new variant of real quantifier elimination. Given a first-order formula and a real point we compute a quantifier-free formula which is not only for the given point equivalent to the input formula but also for all points in a semi-algebraic set containing the specified point. The description of this semi-algebraic set is explicitly computed in the form of a conjunction of atomic formulas. Local quantifier elimination is in its application area superior to both regular and generic quantifier elimination due to faster running times and shorter results.

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OpenAlex reports 6 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We introduce local quantifier elimination as a new variant of real quantifier elimination. Given a first-order formula and a real point we compute a quantifier-free formula which is not only for the given point equivalent to the input formula but also for all points in a semi-algebraic set containing the specified point. The description of this semi-algebraic set is explicitly computed in the form of a conjunction of atomic formulas. Local quantifier elimination is in its application area superior to both regular and generic quantifier elimination due to faster running times and shorter results.

Key concepts: Quantifier elimination, Quantifier (linguistics), Mathematics, Set (abstract data type), Point (geometry), Algebraic number, Discrete mathematics, Algebra over a field

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