Compressibility of infinite binary sequences
It is known that infinite binary sequences of constant Kolmogorov complexity are exactly the recursive ones. Such a kind of statement no longer holds in the presence of resource bounds. Contrary to what intuition might suggest, there are sequences of constant, polynomial-time bounded Kolmogorov comp...
| Autores: | , , |
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| Tipo de recurso: | informe técnico |
| Fecha de publicación: | 1996 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/82554 |
| Acceso en línea: | https://hdl.handle.net/2117/82554 |
| Access Level: | acceso abierto |
| Palabra clave: | Kolmogorov complexity Infinite binary sequences Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica |
| Sumario: | It is known that infinite binary sequences of constant Kolmogorov complexity are exactly the recursive ones. Such a kind of statement no longer holds in the presence of resource bounds. Contrary to what intuition might suggest, there are sequences of constant, polynomial-time bounded Kolmogorov complexity that are not polynomial-time computable. This motivates the study of several resource-bounded variants in search for a characterization, similar in spirit, of the polynomial-time computable sequences. We propose some definitions, based on Kobayashi's notion of compressibility, and compare them to both the standard resource-bounded Kolmogorov complexity of infinite strings, and the uniform complexity. Some nontrivial coincidences and disagreements are proved. The resource-unbounded case is also considered. |
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