## ABSTRACT

Last chapter introduces an approach that can obtain a maximally permissive livenessenforcing supervisor with the minimal number of control places. It is a non-iterative approach since all control places can be obtained by solving an ILPP once (which is denoted as MCPP in Chapter 7). Though this approach overcomes the problems of both behavioral permissiveness and structural complexity, it still suers from expensive computational costs. Solving an ILPP is NP-hard in theory and greatly depends on the number of constraints and variables in it. For a large-scale Petri net model, the ILPP designed by this approach may have a huge number of constraints and integer variables, which cannot be solved within a reasonable time. For instance, in Chapter 7, the ILPP for a Petri net model from (Ezpeleta et al., 1995) with 26 places and 20 transitions has 15,640 constraints and 1,700 variables. It takes 44 hours to solve it.