  It is argued that transformation processes (generation rules) showing
evidence of a long evolutionary history in universal computing systems can be
generalized. The explicit function class $ \Omega $ is defined as follows:
"Operators whose eigenvectors (or eigenvalues) have an irrational number in
their components constitute a class of functions with quasi-periodic structure,
$ \Omega $, and the class $ \Omega $ shows evidence of a long evolutionary
history." In order to empirically prove this theorem by examining physical
systems carrying out life activities or intellectual outputs of developed
intelligence, the basic framework of the universal machine model C and the
computational language $ \beta $ is presented as a model for general
computational methods, which allow transformation processes (generation rules)
with deep algorithmic complexity to be derived from generation results. C and $
\beta $ perform massively parallel computations on event-state systems
consisting of exponential combinations of propositional elements expressed in
terms of correlations between subsystems. The logical structure of the
computational language relies on a non-distributivity in Hilbert spaces or
orthogonal modular lattices, allowing for the manipulation and deduction of
simultaneous propositions. In this logical local structure, the propositions
implying certain consequences are not uniquely determined.
