On improving efficiency of model checking through systematically ...

The example in Figure 3.8 is simple because there is no constraint (assertion)
on b1,b2 and thus there is no guard on transitions in the input
graph. However, it is often the case that the assertion contrains the values
of input variables. For example:
assertion
(a1 and b1 and b2) or
(not a2 and b1) or
(a1 and a2 and b2)
In this example, a1,a2 are state variables and b1,b2 are input variables.
Now we have to specify how b1,b2 are set using the above assertion.
First, we explicitly state the condition for combinations between b1,b2,
meaning that the Boolean expression in the above assertion is transformed
to the following equivalent expression:
(a1 and b1 and b2) or
(not a2 and b1 and b2) or
(not a2 and b1 and not b2) or
(a1 and a2 and b1 and b2) or
(a1 and a2 and not b1 and b2)
Then we group conditions according to combinations of b1,b2. Weget
the following expression:
((a1 or (not a2) or (a1 and a2)) and (b1 and b2)) or
((not a2) and (b1 and not b2)) or
((a1 and a2) and (not b1 and b2)) or
(not b1 and not b2)
Note that the last case (not b1 and not b2) is not stated anywhere
in the assertion. That means b1 and b2 can be both false without any
constraint. The final input graph of the example is presented in Figure 3.9.
In addition to those aforementioned adaptions, we introduce an additional
location to play as the fake initial location and create a transition
from this location to the truly initial location so that input variables can be
setproperlyatthestartofexecution.
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