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A foundation for real recursive function theory [PDF]

open access: bronzeAnnals of Pure and Applied Logic, 2009
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
openalex   +4 more sources

Recursive and nonextendible functions over the reals; filter foundation for recursive analysis.II [PDF]

open access: bronzeAnnals of Pure and Applied Logic, 1999
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Iraj Kalantari, Lawrence Welch
openalex   +3 more sources

Stateful InREC: Stateful In-Network Real Number Computation With Recursive Functions

open access: greenIEEE Transactions on Network and Service Management, 2022
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
openalex   +4 more sources

Inferability of recursive real-valued functions [PDF]

open access: green, 1997
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
openalex   +2 more sources

Refutability and Reliability for Inductive Inference of Recursive Real-Valued Functions

open access: diamondIPSJ Digital Courier, 2005
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
openalex   +3 more sources

The Complexity of Real Recursive Functions [PDF]

open access: closed, 2002
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
openalex   +2 more sources

On a theory of computation and complexity over the real numbers: 𝑁𝑃- completeness, recursive functions and universal machines [PDF]

open access: diamondBulletin of the American Mathematical Society, 1989
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
openalex   +4 more sources

Three simulations of Turing machines with the use of real recursive functions

open access: greenAnn. UMCS Informatica, 2004
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
  +6 more sources

Elementarily computable functions over the real numbers andR-sub-recursive functions

open access: closedTheoretical Computer Science, 2005
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
  +4 more sources

Convergence of a Recursive Identifier Using Positive Real Transfer Function

open access: bronzeTransactions of the Society of Instrument and Control Engineers, 1982
Katsunobu Konishi   +3 more
openalex   +3 more sources

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