On improving efficiency of model checking through systematically ...

Hence, if we limit the length of the sequence of input variables, there
could be several cases in which only the transition to get input values
again is taken instead of a real transition action in the system. Therefore,
modeling the restriction in this way does not help to show the
actual workload of Uppaal in the verification.
Although the aforementioned solution does help to make Uppaal finish
the verification, it does not solve the problem at its root since doing that way
means we only verify a small part of the real state space. We are looking
for a solution to remodel the Nbac output model in such a way that the
resulting model becomes finite for Uppaal. Solving the verification problem
for infinite systems is a research problem that is still on progress in many
research groups. For such systems, theorem proving has been relied on[20,
18]. Abstraction techniques have also been used to solve that problem[9, 14,
10]. However, we ran out of time for any further investigation.
5.4 Summary
We have presented experimental results that we obtained on the verification
of abstract models of case studies. Uppaal could finish verification on the
tiny example and the asynchronous reader/writer algorithm in a short time.
However, it could not verify the Fischer’s protocol and Subway system.
We measured the memory usage in the verification for a range of number
of iterations around the good location that the system can take. It turned
out that the memory usage grew very quickly and thus state space explosion
was unavoidable. We investigated the problem through several trials to
figure out the reason for the state space explosion. The reason is that those
systems are infinite due to the unlimited increment of Integer variables and
thus the fixed point can not be reached. Uppaal will only terminate verification
when it reaches the bounded integer value. However, the memory
resource was exhausted before Uppaal could reach that limit when model
checking the Fischer’s protocol and Subway system.
We tried to solve the problem by restricting the number of iterations so
that Uppaal can finish the verification. Among two different ways to do it,
we chose to implement the counter and limit the value of the counter in the
system graph.
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