An improved maximally permissive deadlock prevention policy based on the theory of regions and reduction approach

The theory of regions has been recognised as the powerful method of deadlock prevention policy for obtaining maximally permissive controllers. It is well known that all legal and live maximal behaviour of Petri net models can be preserved by using marking/transition-separation instances (MTSIs) or event-state-separation-problem (ESSP) methods. However, they encountered great difficulties in solving all sets of inequalities that is an extremely time-consuming problem. Moreover, the number of linear programming problems (LPPs) of legal markings is also exponential with net size when a plant net grows exponentially. This work proposes a novel methodology to reduce the number of MTSIs, ESSPs and LPPs. To do so, the reachability condition equations in the theory of region can be reduced under the reduction approach. The problem of LPPs can then be reduced. Additionally, crucial marking/transition-separation instances is developed in our deadlock prevention policy that allows designers to employ few MTSIs to deal with deadlocks. The advantage of the proposed policy is that a maximally permissive controller can be obtained with drastically reduced computation. Finally, experimental results infer that our proposed policy seems to be the most efficient policy among existing methods.