Improvement on 'A merging method for the siphon-based flexible manufacturing systems maximally permissive controllers with simpler structures'

Recent maximally permissive deadlock prevention controls for systems of simple sequential processes with resources (S3PR) also aim at constructing simplest structures in the shortest amount of time for flexible manufacturing systems modelled by Petri nets. The paper in Liu et al. (2013, IMA J. Math. Control Inf., doi: 10.1093/imamci/dnt029) proposes a method to merge several monitors into a single one while not losing the live states. It achieves the same best results in the existing literature while avoiding the time-consuming reachability analysis which does not scale well with the large size of the nets. For a well-known benchmark, the method needs one more monitor than other approaches. Thus, siphon-based merging may not achieve minimal configuration. Although we could reduce one monitor, which monitor to choose to merge seem to be ad hoc. It is unclear how to select a monitor to reduce for large nets. This paper tackles such an issue successfully.