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On the information carried by programs about the objects they compute
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.
Cited literature [20 references]
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
Long-term archiving on: : Wednesday, December 24, 2014 - 8:58:12 PM
Contributor : Mathieu Hoyrup <>
Submitted on : Tuesday, September 23, 2014 - 4:51:54 PM
Last modification on : Tuesday, December 18, 2018 - 4:48:02 PM
Long-term archiving on: : Wednesday, December 24, 2014 - 8:58:12 PM
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