A foundation for real recursive function theory [PDF]
The class of recursive real functions, REC\((\mathbb R)\), is defined as the smallest set containing the constant functions 0, 1, and \(-1\), the projection functions, and closed under composition, aggregation, differential recursion, and the lim sup operator.
José Félix Costa +2 more
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Recursive and nonextendible functions over the reals; filter foundation for recursive analysis.II [PDF]
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Iraj Kalantari, Lawrence Welch
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Stateful InREC: Stateful In-Network Real Number Computation With Recursive Functions
Current generation of Reconfigurable Match-Action Tables switches are highly programmable, able to support stateful operations and pipeline specifications using languages like P4. Nevertheless, these switches do not offer primitives to support real-valued operations on the data plane, thus requiring support from external servers or middle boxes to ...
Matthews Jose +3 more
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Inferability of recursive real-valued functions [PDF]
This paper presents a metod of inductive inference of realvalued functions from given pairs of observed data of (x,h(x)), where h is a target function to be inferred. Eac of suc observed data inevitably involves some ranges of errors, and hence it is usually represented by a pair of rational numbers sow te approximate value and te error bound ...
Eiju Hirowatari, Setsuo Arikawa
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Refutability and Reliability for Inductive Inference of Recursive Real-Valued Functions
Inductive inference gives us a theoretical model of concept learning from examples. In this paper, we study refutably and reliably inductive inference of recursive real-valued functions. First we introduce the new criteria RealRefEx for refutable inference and RealRelEx for reliable inference.
Eiju Hirowatari +3 more
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The Complexity of Real Recursive Functions [PDF]
We explore recursion theory on the reals, the analog counterpart of recursive function theory. In recursion theory on the reals, the discrete operations of standard recursion theory are replaced by operations on continuous functions, such as composition and various forms of differential equations.
Manuel L. Campagnolo
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On a theory of computation and complexity over the real numbers: 𝑁𝑃- completeness, recursive functions and universal machines [PDF]
A model for computation over the reals \({\mathbb{R}}\) (or an arbitrary ordered ring \({\mathcal R})\) is presented. A machine over \({\mathcal R}\) is a digraph with two kinds of nodes: computation (fan-out 1) nodes labelled by polynomial maps \({\mathfrak g}: {\mathcal R}^ n\to {\mathcal R}^ n\), and branching (fan-out 2) nodes labelled by tests ``\(
Lenore Blum, M. Shub, Steve Smale
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Three simulations of Turing machines with the use of real recursive functions
Artykuł z : Annales Universitatis Mariae Curie-Skłodowska, Sectio AI, Informatica, Vol. 2 (2004), s. 101-114 ; Artykuł z : Annales Universitatis Mariae Curie-Skłodowska, Sectio AI, Informatica, Vol. 2 (2004), s.
Monika Piekarz
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Elementarily computable functions over the real numbers and
An algebraic characterization of elementarily computable functions over the real numbers in the sense of recursive analysis is presented in this paper. Main result: For any function \(f\) over the real numbers being 2-times continuously differentiable defined on a product of compact interval with rational endpoints, \(f\) is elementarily computable in ...
Olivier Bournez, Emmanuel Hainry
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Convergence of a Recursive Identifier Using Positive Real Transfer Function
Katsunobu Konishi +3 more
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