Using heaps-of-pieces in synthesis of time optimal supervisors

In many practical applications we need to compute a nonblocking supervisor that not only complies with pre-specified safety requirements but also achieves a certain time optimal performance such as maximum throughput. In this paper we first present a minimum-makespan supervisor synthesis problem. Then we show that the problem can be solved by a terminable algorithm, where the execution time of each string is computable by the theory of heaps-of-pieces.