It has been a hot research topic to synthesize maximally permissive controllers with fewest monitors. So far, all maximally permissive control models for a well-known benchmark are generalized Petri net, which com-plicates the system. In addition, they all relied on time-consuming reachability analysis. Uzam and Zhou ap-ply First-met-bad-marking (FBM) method to the benchmark to achieve a near maximal permissive control policy with the advantage of no weighted control (WC) arcs. To improve the state of the art, it is interesting to synthesize optimal controller with as few weighted arcs as possible since it is unclear how to optimize the control for siphon involving WC arcs, This paper explores the condition to achieve optimal controller with-out WC and defining a new type of siphon, called α-siphon. If the condition is not met, one can apply the technique by Piroddi et al. to synthesize optimal controllers with WC.
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