### Table 3: Petri net minimization.

1998

"... In PAGE 29: ... Therefore, automatic techniques to produce succint representations of the same system can be useful. Table3 describes the results of the application of our algorithms to the minimization of a given labeled Petri net. The examples correspond to speci cations of asynchronous circuits that have been produced manually by system designers.... In PAGE 29: ... P, T, F and M are the numbers of places, transitions, arcs and markings respectively. Figure 16 depicts the initial and nal Petri net for the example future shown in Table3 . The nal result illustrates how powerful the synthesis techniques can be in nding compact representa- tions of the same behavior.... ..."

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### Table 3: Petri net minimization.

1998

"... In PAGE 30: ... Therefore, automatic techniques to produce succint representations of the same system can be useful. Table3 describes the results of the application of our algorithms to the minimization of a given labeled Petri net. The examples correspond to speci cations of asynchronous circuits that have been produced manually by system designers.... In PAGE 30: ... P, T, F and M are the numbers of places, transitions, arcs and markings respectively. Figure 16 depicts the initial and nal Petri net for the example future shown in Table3 . The nal result illustrates how powerful the synthesis techniques can be in nding compact representa- tions of the same behavior.... ..."

### Table 1: Reachable markings for the Petri net of Figure 3

"... In PAGE 5: ... If t is an EXP transition, the transition between ma and mc will have a constant rate given by: ac = Pbc X t2 quot;(mi) t where quot;(mi) is the set of EXP transitions enabled in mi and t is their ring rate. As an example of the generation of the extended and reduced reachability graph, consider a system based on a client-server paradigm, whose Petri net model is shown in Figure 3 while the reachable markings are identi ed in Table1... ..."

### Table 4: Reachable markings for the Petri net of Figure 9

1998

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### Table 1. Encoding for the places and reachable markings of the Petri net in Fig. 7.

### Table 1: Previous techniques for CSC of Petri nets

"... In PAGE 2: ... The Unique State Coding (USC) prop- erty, similar to CSC but still more restrictive, has been also used for the same purpose. Table1 summarizes the most signi cant e orts in the area of CSC for Petri nets. Among the di erent subclasses of Petri nets, algorithms have been proposed for Marked Graphs (MGs) [Van90, KKT91], Free Choice nets [LMBSV92], and general Petri nets [VLGM92].... ..."

### Table 2: Reachability set for the Petri net of Figure 2

1998

"... In PAGE 9: ... To understand the previous analysis better we can examine, for instance, the Petri net shown in Figure 2; its complete reachability graph is shown in Figure 3 a) and the reduced reachability graph in Figure 3 b). For this network we also give the reachability set ( Table2 ), in which we have used * to indicate the vanishing markings. In the marking m2 (tokens in places p2 and p3) the two transitions g1 and g2 are enabled, and the sets of states mentioned above can be identi ed.... ..."

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### Table 1. Sets of deadlocks and traps of the Petri net shown in Fig. 1.

"... In PAGE 3: ... 1 contains 10 deadlocks and 10 traps (excluding the entire set of places, which is both a deadlock and a trap). In Table1 all those dead- locks and traps are listed; minimal deadlocks and traps are marked. Table 1.... In PAGE 5: ... Of course, for reduced search trees this relation may differ. In Table1 the results of computer experiments are shown. Now let us turn to the pruning rules.... ..."

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