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What Percentage of Programs Halt?

Abstract : Fix an optimal Turing machine U and for each n consider the ratio ρ^U_n of the number of halting programs of length at most n by the total number of such programs. Does this quantity have a limit value? In this paper, we show that it is not the case, and further characterise the reals which can be the limsup of such a sequence ρUn. We also study, for a given optimal machine U, how hard it is to approximate the domain of U from the point of view of coarse and generic computability.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-01279151
Contributor : Alexander Shen <>
Submitted on : Thursday, February 25, 2016 - 2:51:51 PM
Last modification on : Friday, March 27, 2020 - 3:55:45 AM

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Laurent Bienvenu, Damien Desfontaines, Alexander Shen. What Percentage of Programs Halt?. ICALP: International Colloquium on Automata, Languages and Programming, EATCS, Jul 2015, Kyoto, Japan. pp.219-230, ⟨10.1007/978-3-662-47672-7⟩. ⟨lirmm-01279151⟩

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