Summary: Tools for Controller Synthesis of Timed Systems
Verification is the problem of checking whether the behavior of a closed system satisfies a given property.
The system is closed in the sense that its behavior is fully specified. Synthesis is the problem of finding a
way to "close" an open system, so that the behavior of the closed system satisfies a given property. The
system is open in the sense that its behavior is under-specified: it can be modified (restricted) during the
synthesis process. Closing a system usually means coupling it with a controller which observes the behavior
of the system so far and restricts it by disabling or forcing some actions. The controller is state-feedback
when its decisions depend solely on the current state of the system.
In this paper, we present two tools for (state-feedback) controller synthesis of timed systems. Our model
is based on timed automata  with discrete actions annotated as controllable or uncontrollable. Controllable
actions can be restricted, while uncontrollable cannot. Following the approaches of [23, 7, 3] we associate
urgency with actions rather than states. We are interested in controllers ensuring two types of properties,
namely, invariance or inevitability. Invariance means that all behaviors of the closed system remain within
a given set of states. Inevitability means that all behaviors of the closed system reach a given set of states.
We present our model and define the synthesis problems in Section 2.
The first tool we present is called SynthKro. It is a module of the tool suite Kronos [12, 8]. SynthKro is
based on the notion of controllable states, which are computed using a backward fixpoint iteration of special