• Algorithmic complexity as a cr...

Treffer: Algorithmic complexity as a criterion of unsolvability

Title:
Algorithmic complexity as a criterion of unsolvability
Authors:
BURGIN, Mark
Source:
Complexity of algorithms and computationsTheoretical computer science. 383(2-3):244-259
Publisher Information:
Amsterdam: Elsevier, 2007.
Publication Year:
2007
Physical Description:
print, 23 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Logique mathématique, fondements, théorie des ensembles, Mathematical logic, foundations, set theory, Logique et fondements, Logic and foundations, Récursivité, Recursion theory, Sciences appliquees, Applied sciences, Informatique; automatique theorique; systemes, Computer science; control theory; systems, Informatique théorique, Theoretical computing, Automates. Machines abstraites. Machines de turing, Automata. Abstract machines. Turing machines, Algorithmique. Calculabilité. Arithmétique ordinateur, Algorithmics. Computability. Computer arithmetics, Divers, Miscellaneous, Algorithme récursif, Recursive algorithm, Algoritmo recursivo, Algorithmique, Algorithmics, Algorítmica, Calculabilité, Computability, Calculabilidad, Complexité algorithme, Algorithm complexity, Complejidad algoritmo, Décidabilité, Decidability, Decidibilidad, Entrée ordinateur, Input, Entrada ordenador, Fonction récursive, Recursive function, Función recursiva, Informatique théorique, Computer theory, Informática teórica, Machine Turing, Turing machine, Máquina Turing, Ordre 1, First order, Orden 1, 03D20, 03Dxx, 68Q05, 68Q30, 68Wxx, Complexité Kolmogorov, Kolmogorov complexity, Algorithmic problem, Inductive Turing machine, Inductive algorithmic complexity, Recursive algorithmic complexity, Super-recursive algorithm
Document Type:
Konferenz Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Department of Mathematics, University of California, Los Angeles, 405 Hilgard Ave, Los Angeles, CA 90095, United States
ISSN:
0304-3975
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=19061047
Rights:
Copyright 2008 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:
Computer science; theoretical automation; systems

Mathematics
Accession Number:
edscal.19061047
Database:
PASCAL Archive

Weitere Informationen

There is a dependency between computability of algorithmic complexity and decidability of different algorithmic problems. It is known that computability of the algorithmic complexity C(x) is equivalent to decidability of the halting problem for Turing machines. Here we extend this result to the realm of superrecursive algorithms, considering algorithmic complexity for inductive Turing machines. We study two types of algorithmic complexity: recursive (classical) and inductive algorithmic complexities. Relations between these types of algorithmic complexity and decidability of algorithmic problems for Turing machines and inductive Turing machines are considered. In particular, it is demonsrated that computability of algorithmic complexity is equivalent not only to decidability of the halting problem, but also to decidability by inductive Turing machines of the first order of many other problems for Turing machines, such as: if a Turing machine computes a recursive (total) function; if a Turing machine gives no result only for n inputs; if a Turing machine gives results only for n inputs.