  The optimal prefix-free machine U is a universal decoding algorithm used to
define the notion of program-size complexity H(s) for a finite binary string s.
Since the set of all halting inputs for U is chosen to form a prefix-free set,
the optimal prefix-free machine U can be regarded as an instantaneous code for
noiseless source coding scheme. In this paper, we investigate the properties of
optimal prefix-free machines as instantaneous codes. In particular, we
investigate the properties of the set U^{-1}(s) of codewords associated with a
symbol s. Namely, we investigate the number of codewords in U^{-1}(s) and the
distribution of codewords in U^{-1}(s) for each symbol s, using the toolkit of
algorithmic information theory.
