Differentiability of Polynomials over Reals

Differentiability of Polynomials over Reals

δ-Decidability over the Reals∗

Given any collection F of computable functions over the reals, we show that there exists an algorithm that, given any LF -sentence φ containing only bounded quantifiers, and any positive rational number δ, decides either “φ is true”, or “a δ-strengthening of φ is false”’. Under mild assumptions, for a C-computable signature F , the δ-decision problem for bounded Σk-sentences in LF resides in (Σ...

Concurrent Cooperating Solvers over Reals

Systems combining an interval narrowing solver and a linear programming solver can tackle constraints over the reals that none of these solvers can handle on their own. In this paper we introduce a cooperating scheme where an interval narrowing solver and a linear programming solver work concurrently. Information exchanged by the solvers is therefore handled as soon as it becomes available. Mor...

Reconstruction of ΣΠΣ(2) Circuits over Reals

Reconstruction of arithmertic circuits has been heavily studied in the past few years and has connections to proving lower bounds and deterministic identity testing. In this paper we present a polynomial time randomized algorithm for reconstructing ΣΠΣ(2) circuits over R, i.e. depth−3 circuits with fan-in 2 at the top addition gate and having real coefficients. The algorithm needs only a blockb...

Hierarchies of total functionals over the reals

We compare two natural constructions, the A-hierarchy and the R-hierarchy, of hereditarily total, continuous and extensional functionals of ,nite types over the reals. The A-hierarchy is based on the closed interval domain representation of the reals while the R-hierarchy is based on the binary negative digit representation. We show that the two hierarchies share a common maximal core. To this ...