On improving efficiency of model checking through systematically ...

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Memory usage plot of the verification on subway example
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Figure 5.2: Memory usage of the experiment for the subway system
model was significant for Uppaal to verify. We tried to identify the specific
reason for such a large state space.
The first reason might be the physical size (defined in Chapter 4) of the
model. However, a comparison between abstract models of Fischer’s protocol,
Asychronous reader/writer algorithm and Subway system showed that
physical size was not the real reason. Table 5.2 presents that comparison.
Although the model of Asynchronous reader/writer algorithm contains a
large number of variables and Boolean operators, we can still get conclusive
verificiation result for that algorithm.
System Shared vars Input vars Locations Edges Bool opt
Fischer-2 12 3 3 3 2117
Subway-2-p1 13 3 3 3 336
Asyn. w/r alg. 32 0 3 3 59484
Table 5.2: Comparison between three models
From the above comparison, we noticed that the difference in the number
of input variables between those systems could be a reason for large
state space especially when input variable involved non-deterministic factor.
Remind that in an XTG model, the values generated using the input
graph control the behavior of the system. However, taking a closer look at
the input graph and doing the math, we see that although values of input
variables are assigned non-deterministically, the total number of cases to
assign input values are finite. Figure 5.3 depicts this argument.
The right graph in Figure 5.3 is the input graph. It generates two values
0 and 1 in a non-deterministic manner for the system graph on the left. The
system graph specifies that if b is larger than 1, the system will go to end.
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