Treffer: Nonlinear phenomena in spaces of algorithms

Title:
Nonlinear phenomena in spaces of algorithms
Authors:
BURGIN, M
Source:
International journal of computer mathematics. 80(12):1449-1476
Publisher Information:
Abingdon: Taylor and Francis, 2003.
Publication Year:
2003
Physical Description:
print, 1 p.1/4
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Algèbre, Algebra, Systèmes algébriques généraux, General algebraic systems, Géométrie, Geometry, Géométrie convexe et discrète, Convex and discrete geometry, Algorithme récursif, Recursive algorithm, Algoritmo recursivo, Algorithme, Algorithm, Algoritmo, Algorithmique, Algorithmics, Algorítmica, Base, Calcul automatique, Computing, Cálculo automático, Calculabilité, Computability, Calculabilidad, Chaos, Caos, Espace linéaire, Linear space, Espacio lineal, Machine Turing, Turing machine, Máquina Turing, Modèle mathématique, Mathematical model, Modelo matemático, Non linéarité, Nonlinearity, No linealidad, Problème, Problem, Problema, Processus non linéaire, Non linear process, Proceso no lineal, Puissance, Power, Potencia, Relation, Relación, Résultat, Result, Resultado, Système hiérarchisé, Hierarchical system, Sistema jerarquizado, Algorithme super récursif, Super recursive algorithm, Diagramme commutatif, Commutative diagram, Espace calculabilité, Computability space, Hiérarchie arithmétique, Arithmetical hierarchy
Subject Geographic:
Monde, World, Mundo
Document Type:
Fachzeitschrift Article
File Description:
text
Language:
English
Author Affiliations:
Department of Mathematics, University of California, Los Angeles, CA 90095, United States
ISSN:
0020-7160
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=15370842
Rights:
Copyright 2004 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.15370842
Database:
PASCAL Archive

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Nonlinear phenomena, which are so important in nature and society, are considered here in relation to the world of algorithms and computations. To have a mathematical model for this world, formal computability spaces are introduced. It is demonstrated that the traditional approach to algorithms, which is based on such popular models as Turing machines, results in linear subspaces of the computability space. Nonlinear phenomena appear when we go to the more powerful class of such super-recursive algorithms as inductive Turing machines. It is demonstrated how this nonlinearity imports much higher computing power of inductive Turing machines in comparison with conventional Turing machines. This provides a base to consider problems of chaos, emergent computations and infinity from the algorithmic point of view.