What we have seen in the preceding chapters is that Ordered Binary Decision Diagrams can be used as a representation in a wide variety of automatic verification algorithms, in order to cope with the state explosion problem. This can be done in a unified way by representing the algorithms in the Mu-Calculus fixed point notation. For fairly diverse families of regularly structured systems, the CTL model checking algorithm was observed to run in time and space which increased polynomially in the size of the system, while the number of reachable states increased exponentially. These results bear out a theoretical result bounding the OBDD representation of the transition relation for such systems. Standard automatic verification algorithms would be unsuitable for these examples because their complexity is proportional to the number of reachable states.
Unable to display preview. Download preview PDF.