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A deadlock prevention approach for flexible manufacturing systems (FMS) with uncontrollable transitions in their Petri net models (PNM) was proposed in [1]. A few examples were considered to show the applicability of the proposed approach. Fig. 1 depicts the PNM of an FMS considered in [1]. This is a well-known FMS example widely used in the Petri-net based deadlock prevention literature to demonstrate a variety of design methods of liveness-enforcing supervisors [2][3][4][5][6][7][8][9]. In the literature, generally all the transitions of this PNM are assumed to be controllable, but in [1] it is assumed that transitions t1, t2, t7, t11, t15, and t16 are controllable and other transitions are uncontrollable. The PNM shown in Fig. 1 suffers from a deadlock problem and, therefore, to enforce the liveness on this PNM it is necessary to introduce a liveness enforcing mechanism. Consequently, by using the approach proposed in [1] seven monitors (control places) shown in Fig. 2 were computed to enforce liveness on the PNM shown in Fig. 1. However, as it will be shown in the next section, the closed loop system containing the PNM shown in Fig. 1 and the LES shown in Fig. 2 does not provide a live system.The controlled PNM consists of the PNM shown in Fig. 1 and of seven monitors depicted in Fig. 2. In order to analyse the controlled PNM, a Petri net analysis software tool called INA [10] was used. The controlled PNM is obtained as an INA file as shown in Fig. 3. Analysis results for the controlled PNM by using INA is obtained as shown in Fig. 4. It can be seen from Fig. 4 that the controlled PNM is not live. In order to analyse Petri-net-based monitors, a recently proposed method [11] can also be used.This paper has shown that the liveness enforcing supervisor containing seven monitors computed in [1] does not provide a live behaviour.

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In a flexible manufacturing system (FMS) with multiple products, deadlocks can arise due to limited shared resources, such as machines, robots, buffers, fixtures etc. The development of efficient deadlock prevention policies, which can optimise the use of system resources, while preventing deadlocks from occurring, has long been an important issue to be addressed. In [1], an optimal deadlock prevention policy was proposed, based on the use of reachability graph (RG) analysis of the Petri net model (PNM) of a given FMS and the synthesis of a set of new net elements, namely places with initial marking and related arcs, to be added to the PNM, using the theory of regions. The policy proposed in [1] is optimal in the sense that it allows the maximal use of resources in the system according to the production requirements. For very big PNMs, the reachability graph of the PNMs becomes very large and the necessary computations to obtain an optimal deadlock prevention policy become more difficult. In this paper, we propose the use of the Petri net reduction approach to simplify very big PNMs so as to make necessary calculations easily in order to obtain an optimal deadlock prevention policy for FMSs. An example is provided for illustration.

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As automated manufacturing systems become more complex, the need for an effective design tool to produce both highlevel discrete event control systems (DECS)

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