The ideas behind Terras's analysis seem basic to a deeper understanding
of the problem, so I describe them in detail.
In order to do this, I introduce some notation to
describe the results of the process of iterating the function .
Given an integer **n**, define a sequence of **0-1** valued
quantities by
where .
The results of first **k** iterations of **T** are completely described by the
* parity vector*
since the result of **k** iterations is
where
and
Note that in (2.5), (2.6) both and
are completely determined by the parity vector given by
(2.3); I sometimes indicate this by writing
(instead of .
The formula (2.4) shows that a necessary condition for is that
since is nonnegative.
Terras [67] defines the * coefficient stopping time*
to be the least value of **k** such that (2.7) holds,
and if no such value of **k** exists.
It is immediate that
The function plays an important role in the analysis of the
behavior of the stopping time function , see Theorem C.