Supervisory Controller Synthesis for Nonterminating Processes Is an Obliging Game

In this article, we present a new algorithm to solve the supervisory control problem over nonterminating processes modeled as $\omega$-regular automata. A solution to this problem was obtained by Thistle in 1995, which uses complex manipulations of automata. We show a new solution to the problem through a reduction to obliging games, which, in turn, can be reduced to $\omega$-regular reactive synthesis. Therefore, our reduction results in a symbolic algorithm based on manipulating sets of states.