Are faults more or less likely to be hiding after assertions are added and the manner by which test cases are generated changes? We begin to answer this question by looking at the situation where the code has no assertions, and then we will consider the situation where assertions are embedded.
For program P without assertions, we showed that regardless of what
added to test suite D, we know that 
Given a new test suite 
that is not identical
to D and neither test suite is a subset of the other, what can we
say about the relation between 
and 
? Quite
simply, we cannot say anything confidently without running a technique
similar to sensitivity analysis with both D and 
. That is, we do not
know whether 
or 
.
Now let 
represent program P with assertions which were
designed to boost the fault revealing ability of D. Assertions
increase the likelihood that the third condition of the
fault/failure model happens. Then,
>From there, this is also true:
regardless if D and 
have common members. Our argument in
support of this conjecture follows: if the assertions placed into P
(that are based on D) are never exercised via inputs from 
, then
; if as little as one assertion is
exercised by some input in 
, then it is possible that 
will be true.
What this suggests for assertions is straightforward. Since
assertions directly affect propagation, if propagation is homogeneous
for some 
, it is likely to be homogeneous for some other 
.
Whether j is in D
or 
is immaterial. In general then, assertions appear to have an
impact on fault detectability that is without respect for whether the
inputs to the software are from one test suite or another. Hence
since assertions improve the propagation prospects for inputs from D
by increasing the cardinality or dimensionality of the output space,
they should also improve the propagation prospects for 
.
And finally, we suspect that it will generally be true that:
However there will be cases where
specifically when 
and/or the assertions placed
into P are not exercised.
