Abstract
We present a generalisation of the supervisory control problem proposed by Ramadge and Wonham. The objective of that problem is to synthesise a controller which constrains a system's behaviour according to a given specification, ensuring controllability and coaccessibility. By introducing a new representation of the solution using systems of ?-calculus equations we are able to handle these two conditions separately and thus to exchange the coaccessibility requirement by any ?-calculus expression. Well-known results on the complexity of ?-calculus model checking allow us to easily assess the computational complexity of any generalisation. As an example we solve the synthesis problem under consideration of fairness constraints.