On the Information Carried by Programs About the Objects they Compute
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Fecha
2017-11
Autores
Profesor/a Guía
Facultad/escuela
Idioma
en
Título de la revista
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Editor
Springer New York LLC
Nombre de Curso
Licencia CC
CC BY 4.0 DEED
Licencia CC
https://creativecommons.org/licenses/by/4.0/deed.es
Resumen
In computability theory and computable analysis, finite programs can compute infinite objects. Such objects can then be represented by finite programs. Can one characterize the additional useful information contained in a program computing an object, as compared to having the object itself? Having a program immediately gives an upper bound on the Kolmogorov complexity of the object, by simply measuring the length of the program, and such an information cannot usually be derived from an infinite representation of the object. We prove that bounding the Kolmogorov complexity of the object is the only additional useful information. Hence we identify the exact relationship between Markov-computability and Type-2-computability. We then use this relationship to obtain several results characterizing the computational and topological structure of Markov-semidecidable sets. This article is an extended version of Hoyrup and Rojas (2015), including complete proofs and a new result (Theorem 9). © 2016, Springer Science+Business Media New York.
Notas
Indexación: Scopus
Palabras clave
Ershov topology, Kolmogorov complexity, Markov-computable, Representation
Citación
Theory of Computing Systems Volume 61, Issue 4, Pages 1214 - 12361 November 2017
DOI
10.1007/s00224-016-9726-9