On Compositional Approaches for Discrete Event Systems Verification and Synthesis

Doctoral thesis, 2015

Over the past decades, human dependability on technical devices has rapidly increased. Many activities of such devices can be described by sequences of events, where the occurrence of an event causes the system to go from one state to another. This is elegantly modelled by state machines. Systems that are modelled in this way are referred to as discrete event systems. Usually, these systems are highly complex, and appear in settings that are safety critical, where small failures may result in huge financial and/or human losses. Having a control function is one way to guarantee system correctness. The work presented in this thesis concerns verification and synthesis of such systems using the supervisory control theory proposed by Ramadge and Wonham. Supervisory control theory provides a general framework to automatically calculate control functions for discrete event systems. Given a model of the system, the plant to be controlled, and a specification of the desired behaviour, it is possible to automatically compute, i.e. synthesise, a supervisor that ensures that the specification is satisfied. Usually, systems are modular and consist of several components interacting with each other. Calculating a supervisor for such a system in the straightforward way involves constructing the complete model of the considered system, which may lead to the inherent complexity problem known as the state-space explosion problem. This problem occurs as the number of states grows exponentially with the number of components, which makes it intractable to examine the global states of a system due to lack of memory and time. One way to alleviate the state-space explosion problem is to use a compositional approach. A compositional approach exploits the modular structure of a system to reduce the size of the model. This thesis mainly focuses on developing abstraction methods for the compositional approach in a way that the final verification and synthesis results are the same as it would have been for the nonabstracted system. The algorithms have been implemented in the discrete event system software tool Supremica and have been applied to verify and compute memory efficient supervisors for several large industrial models.