Stubborn sets with frozen actions

Most ample, persistent, and stubborn set methods use some special condition for ensuring that the analysis is not terminated prematurely. In the case of stubborn set methods for safety properties, implementation of the condition is usually based on recognizing the terminal strong components of the reduced state space and, if necessary, expanding the stubborn sets used in their roots. In an earlier study it was pointed out that if the system may execute a cycle consisting of only invisible actions and that cycle is concurrent with the rest of the system in a non-obvious way, then the method may be fooled to construct all states of the full parallel composition. This problem is solved in this study by a method that is based on “freezing” the actions in the cycle.