Abstract
Fix an optimal Turing machine U and for each n consider the ratio \(\rho ^U_n\) 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 \(\rho ^U_n\). 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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Bienvenu, L., Desfontaines, D., Shen, A. (2015). What Percentage of Programs Halt?. In: Halldórsson, M., Iwama, K., Kobayashi, N., Speckmann, B. (eds) Automata, Languages, and Programming. ICALP 2015. Lecture Notes in Computer Science(), vol 9134. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47672-7_18
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