On the information carried by programs about the objects they compute

Mathieu Hoyrup 1 Cristobal Rojas 2
1 CARTE - Theoretical adverse computations, and safety
Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
Abstract : In computability theory and computable analysis, finite programs can compute infinite objects. Presenting a computable object via any program for it, provides at least as much information as presenting the object itself, written on an infinite tape. What additional information do programs provide? We characterize this additional information to be any upper bound on the Kolmogorov complexity of the object. 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.
Document type :
Conference papers
Liste complète des métadonnées

Cited literature [20 references]  Display  Hide  Download

https://hal.inria.fr/hal-01067618
Contributor : Mathieu Hoyrup <>
Submitted on : Tuesday, September 23, 2014 - 4:51:54 PM
Last modification on : Tuesday, December 18, 2018 - 4:48:02 PM
Document(s) archivé(s) le : Wednesday, December 24, 2014 - 8:58:12 PM

File

withproofs.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01067618, version 1

Collections

Citation

Mathieu Hoyrup, Cristobal Rojas. On the information carried by programs about the objects they compute. STACS15, Mar 2015, Munich, Germany. ⟨hal-01067618⟩

Share

Metrics

Record views

420

Files downloads

116