  We show that real-value approximations of Kolmogorov-Chaitin (K_m) using the
algorithmic Coding theorem as calculated from the output frequency of a large
set of small deterministic Turing machines with up to 5 states (and 2 symbols),
is in agreement with the number of instructions used by the Turing machines
producing s, which is consistent with strict integer-value program-size
complexity. Nevertheless, K_m proves to be a finer-grained measure and a
potential alternative approach to lossless compression algorithms for small
entities, where compression fails. We also show that neither K_m nor the number
of instructions used shows any correlation with Bennett's Logical Depth LD(s)
other than what's predicted by the theory. The agreement between theory and
numerical calculations shows that despite the undecidability of these
theoretical measures, approximations are stable and meaningful, even for small
programs and for short strings. We also announce a first Beta version of an
Online Algorithmic Complexity Calculator (OACC), based on a combination of
theoretical concepts, as a numerical implementation of the Coding Theorem
Method.
