2 Why We Need Model-Based Testing

156 Modeling Systems with Structured State
This kind of model program is finitely branching. In other words, there are only
a finite number of transitions available in each state. As the example shows, even a
finitely branching model may have a computationally infeasible number of states.
We will show in Chapter 11 how to adapt our analysis techniques to cases like this.
In this chapter we’ll focus on how to write model programs that benefit from the
descriptive power of richer structural data types.
It is also possible to write model programs that are not finitely branching. Surprisingly,
this does not necessarily mean that the number of states is unbounded. For
example, here is a model program with only five states that has (computationally)
infinite branching:
namespace Counter2
{
static class Contract
{
static int counter = 0;
}
}
[Action]
static void ModularIncrement(int x)
{ counter = (counter + x) % 5; }
This model program is infinitely branching because in every state there are an
“infinite” (very large) number of integer values for the parameter x. There are only
five states because the modulus operator % in this example limits the counter to five
values.
The previous two examples illustrate one of the main differences between model
programs and finite state machines (FSMs). FSMs always have a finite number
of states and transitions, while model programs may represent systems with an
unbounded number of states and transitions.
You can understand this difference by analogy. Consider the relationship between
the string array type string[] and an enumerator of strings IEnumerator.
Conceptually, the two types are similar, but the string array is a finite type that
provides a Length operation and random, indexed access. The enumerator, on the
other hand, has a more limited interface that does not support querying for the
number of elements or for random access. Instead, the enumerator allows you to get
the first element in the enumeration and each successive element in turn. There is
no requirement that the number of elements in the enumerator be finite.
Similarly, a data structure for an FSM provides operations that allow you to query
for the number of states and transitions. A model program, in contrast, has a more
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