Partial Order Reduction for Timed Actors

We propose a compositional approach for the Partial Order Reduction (POR) in the state space generation of asynchronous timed actors. We define the concept of independent actors as the actors that do not send messages to a common actor. The approach avoids exploring unnecessary interleaving of executions of independent actors. It performs on a component-based model where actors from different components, except for the actors on borders, are independent. To alleviate the effect of the cross-border messages, we enforce a delay condition, ensuring that an actor introduces a delay in its execution before sending a message across the border of its component. Within each time unit, our technique generates the state space of each individual component by taking its received messages into account. It then composes the state spaces of all components. We prove that our POR approach preserves the properties defined on timed states (states where the only outgoing transition shows the progress of time). We generate the state space of a case study in the domain of air traffic control systems based on the proposed POR. The results on our benchmarks illustrate that our POR method, on average, reduces the time and memory consumption by 76 and 34%, respectively.