2 Why We Need Model-Based Testing

0
A()
1
B(2)
2
Systems with Finite Models 123
Figure 7.6. Model program M1.
shared actions that have the same name in two or more of the composed programs
are one action in the product. They execute together, and can only execute when all
of the actions are simultaneously enabled in each of their programs.
The requirement in composition that shared actions must be enabled simultaneously
in every composed program where they occur often has the effect of restricting
behavior, eliminating some runs. That is why composition is useful for scenario control.
Composition restricts behavior to the intersection of the runs of each composed
program. In other words, the runs of the product are the runs that are allowed by
every one of the composed programs. 1
However, there is an important exception: Actions that are not shared can interleave
in any order in the product, and can execute whenever they are enabled in
their own programs. If you wish to suppress this interleaving, you must add those
actions to the other model programs (so there are no longer any unshared actions),
and disable those actions in every state in the other model programs.
To summarize: Under composition, model programs synchronize steps for shared
actions and interleave actions not found in their common action vocabulary.
Here is a small example. M1 and M2 are model programs; for this discussion it is
most helpful to show the FSM of each program. M1 has actions A() and B(2) that
make transitions from the initial state 0 to state 1 to the accepting state 2 (Figure 7.6).
M2 has actions B() and C() that make transitions from state 0 to 1 and back again;
here state 0 is both the initial state and the accepting state (Figure 7.7). Their product
M1 × M2 appears in Figure 7.8. All three actions appear in the product.
1 Composition of model programs is a generalization of the construction of finite automata for
the intersection of regular languages. For example, see the discussion following Theorem 3.3
on pp. 59–60 of Hopcroft and Ullman (1979).
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