Definition 4.17 (TM-Induced Semimeasures
)
Given some TM
,
for
define
.
Again we deviate a bit from Levin's
-oriented path
[
45] (survey: [
30, p. 245 ff, p. 272 ff])
and extend
to
, where we define
.
If
denotes a set of TMs with universal element
, then we write
|
(31) |
Corollary 4.2
For
,
is a CEM and approximable as the difference of two c.e. values:
for
without any 0-bit, otherwise
|
(33) |