## 1 Introduction
[39; 40; 41] proposed one novel technology called MFFP (i.e., the maximal number of forbidding first bad marking (FBM) problem) to obtain maximally permissive reachable markings with very a smaller number of controllers based on Place Invariant (PI) [17] and reachability graph analysis methods. It successfully solves the problem of the excessive consumption of time. It is so pity, when the complexity of one flexible manufacturing system increases, the computational burden raises rapidly. Besides, under our survey the MFFP could just be applied in some special net, outside S\({}^{3}\)PR (The Systems of Simple Sequential Processes with Resources) [10] the method would be failed. Therefore, in author's previous paper [42] the author proposes one iterative deadlock prevention policy to circumvent its disadvantage of conventional MFFP. Besides, the author also proposes one computational improved deadlock concept called IMFFP [43] to enhance MFFP's computational efficiency. [PERSON] et al. [44] firstly introduced the concept of transition-based deadlock prevention policy in their paper, but not the optimal method yet, due to its manual designing process and low control efficiency documented in the expansion literature [45]. Both have the same feature, which helps little in larger and more complicated system [44; 45]. In the following, [PERSON] et al. [46] developed another transition-based control policy to obtain proper supervisors and propose two different kinds of concepts to recover the deadlock problem of FMS. The first one adopts iteration approach. At each iterative step, one integer linear programming problem (ILPP) is calculated to obtain a transition-based controller until all deadlock markings are recovered. The second stage is one-time skill that can find and pick up all transition-based controllers. Although [PERSON] et al. claim that the policy can be applied to all classes of FMS, according to [47],it suffers from the computation complexity problem, since there are too many constraints and variables in the formulated ILPPs. Besides, [PERSON] et al. [48] presented an iteration procedure to design a deadlock prevention policy via control transition constraints. In their work, the structural property of Petri net models is considered for preventing the state explosion problem in reachability graph analysis. Then the controlling transitions are generated and attached to the model to raise up system activity. Nevertheless, this method is still suboptimal since it does not recover system completely. [PERSON] and [PERSON] [49] propose one improved concept to solve system's deadlock problem based on [44]. This article presents an optimal transition-based recovering policy rather than existing method via control places, which just forbids undesirable deadlock states with disadvantage of reducing system liveness. The brand-new method helps accessing all reachable system states and each of them has activated-able transition, implying enough resources for providing competing process. [PERSON] et al. [47] also adopt the transition-based controllers to solve deadlock problem of FMS based on a vector intersection approach. Next, an iteration is used to calculate one small number of recovery controllers to recover all illegal markings. On the other hand, many experts devote some new concept for the deadlock prevention domain of flexible manufacturing systems [50; 51; 62]. Rather than preventing the system from accessing to undesirable state, in this paper the author firstly presents a new method to recover all deadlock markings by attaching control transitions (CT) to deadlock system. Within reachability graph analysis, transitions connect all reachable markings, in other words, a deadlock state could be re-directed to another legal state by adding a computed CT to the system rather than forbidding the deadlock state. In order to recover deadlock system states, the author adopted the most effective CT for the system.