8. Determinewhether the interval-based distributed algorithm(Figure 11.16) to detect Possibly() will always detect Possibly(), even though the

8. Determinewhether the interval-based distributed algorithm(Figure 11.16) to detect Possibly(φ)

will always detect Possibly(φ), even though the algorithm is correct in principle. If it will not, extend the algorithm to ensure that a solution is always detected if it exists.

Hint: Consider the termination of the execution and the Possibly modality holding just a little before the termination.