Question: [27] Consider discrete distributions. Show that there is a simple distribution that is not lower semicomputable, and there is a distribution that is not simple.

[27] Consider discrete distributions. Show that there is a simple distribution that is not lower semicomputable, and there is a distribution that is not simple.

Comments. Therefore, the simple distributions properly contain the lower semicomputable distributions but do not include all distributions. Source:

this and the next three exercises are from [M. Li and P.M.B. Vit´anyi, SIAM J. Comput., 20:5(1991), 911–935].

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