NuSMV models for traffic lights controlling a crossing of two one-way roads.

The models were built to test the impact of using the FAIRNESS keyword. In our setting, a path is fair iff the green light occurs infinitely often.

• project_without_fairness.smv: no fair paths;
• project.smv: fair paths defined.

In project_without_fairness.smv there are CTL and LTL properties specified to check for fairness. It is expected that those properties will not hold. Besides, an "equivalent" CTL formula for strong fairness was proposed. Strong fairness is expressible in LTL, but not in CTL. The CTL formula will hold even when fair paths are not defined. That is an indication that the formula is not actually checking for strong fairness.

• Properties expressible in both CTL and LTL:

  • SAFETY : "It never happens that the colour is green on both traffic lights"
  • LIVENESS: "If the car is waiting by the traffic light it will eventually cross"
  • FAIRNESS: Green light can occur infinitly often

• Properties only expressible in CTL:

  • NON-BLOCKING: For all states where the light is red there exists a state where the sensor detects a car

• Properties only expressible in LTL:

  • STRONG FAIRNESS: Whenever a car is detected infinitely often then the green light occurs infinitly often