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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.
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Submitted on : Tuesday, September 23, 2014 - 4:51:54 PM
Last modification on : Friday, January 21, 2022 - 3:10:20 AM
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  • HAL Id : hal-01067618, version 1


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



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