On improving efficiency of model checking through systematically ...

Variable declaration. All variables, global and local variables, of an
XTG model are declared in Nbac as global state variables. Since Nbac has a
single namespace, it is possible that there are coincidences on local variable
names in an XTG model. In these cases, names of variables must be changed.
Integer and Boolean variables in an XTG model can be declared the same
way in Nbac model. Clock variables, however, are not supported in Nbac.
We declare them as Integers. Our method to model their real-time notion
is described hereafter.
In Figure 2.2, lock is a shared integer variable between two processes; x
is a local clock variable to represent the clock in each process. In the Nbac
model, lock is modeled by two Boolean variables lock1 and lock2. The
reason for such adaption is that Boolean variables is handled exactly while
Interger variables are approximate in Nbac. Integer variables are approximate
in Nbac because they are abstracted by convex polyhedra. Moreover,
in Fischer’s protocol, lock is used to control the status of the critical section
(lock ∈{0, 1}). Thus, it is natural to model lock like that. Two integer
variables c1,c2 are introduced to model the local clock variable x.
Figure 2.3 shows an updated version of the Fischer’s protocol when it is
specified in Nbac.
lock1 != true
l10
lock1 == false,
lock2 ==false
c1 := 0
l11
c1 < 2
c1 2,
lock1 == true
l13
lock1 := false
lock2 != true
l20
lock2 == 0,
lock1 == 0
c2:=0
l21
c2 < 2
c2 2,
lock2 == true
l23
lock2 := false
Figure 2.3: Two parallel processes in the Nbac updated Fischer’s protocol
Parallel processes. In XTG, we can specify several processes in a system
independently and then simply declare them as parallel processes. In
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