Combining supervisor synthesis and model checking

Model checking and supervisor synthesis have been successful in solving different design problems related to discrete systems in the last decades. In this paper, we analyze some advantages and drawbacks of these approaches and combine them for mutual improvement. We achieve this through a generalization of the supervisory control problem proposed by Ramadge and Wonham. The objective of that problem is to synthesize a supervisor which constrains a system's behavior according to a given specification, ensuring controllability and coaccessibility. By introducing a new representation of the solution using systems of μ-calculus equations, we are able to handle these two conditions separately and thus to exchange the coaccessibility requirement by any condition that could be used in model checking. Well-known results on μ-calculus model checking allow us to easily assess the computational complexity of any generalization. Moreover, the model checking approach also delivers algorithms to solve the generalized synthesis problem. We include an example in which the coaccessibility requirement is replaced by fairness constraints. The paper also contains an analysis of related work by several authors.