### Table 3. Mapping WF net to reactive WF net

2003

"... In PAGE 14: ... This firing rule is not adequate to model behavior of the WF engine, which is modeled through internal transitions. We therefore transform a refined WF net (P, T, F) into a reactive WF net (P, Tinternal, Texternal, F), using the previously introduced distinction between internal and external transitions ( Table3 ). This reactive WF net can be mapped to the original refined WF net using function toPetri.... ..."

Cited by 10

### Table 1: Interface between the Petri Net and Troll Models

"... In PAGE 5: ... In the example, the control system commands the tra c lights to turn on the yellow light. In Table1 , the interface between the models is exemplary shown as a simple relation... ..."

### Table 1: An Example of Petri net reduction on 3- stage PCHB model.

2002

"... In PAGE 7: ... Our future work includes developing heuristics to guide the application of these reduction operations, thereby creating a more fully-automated reduction tool. Table1 shows the number of places/transitions in the in- put model and the percentage of places/transitions that were removed compared to the original model due to the proposed reductions. As shown in Table 1, after the proposed series of reductions, the number of places were reduced by more than half and the number of transitions were reduced by a factor of 6.... In PAGE 7: ... Table 1 shows the number of places/transitions in the in- put model and the percentage of places/transitions that were removed compared to the original model due to the proposed reductions. As shown in Table1 , after the proposed series of reductions, the number of places were reduced by more than half and the number of transitions were reduced by a factor of 6. Thus, using this model in place of its more complicated orignal model for system-level performance analysis would yield a significant run-time improvement.... ..."

Cited by 1

### Table 1: An Example of Petri net reduction on 3- stage PCHB model.

2002

"... In PAGE 7: ... Our future work includes developing heuristics to guide the application of these reduction operations, thereby creating a more fully-automated reduction tool. Table1 shows the number of places/transitions in the in- put model and the percentage of places/transitions that were removed compared to the original model due to the proposed reductions. As shown in Table 1, after the proposed series of reductions, the number of places were reduced by more than half and the number of transitions were reduced by a factor of 6.... In PAGE 7: ... Table 1 shows the number of places/transitions in the in- put model and the percentage of places/transitions that were removed compared to the original model due to the proposed reductions. As shown in Table1 , after the proposed series of reductions, the number of places were reduced by more than half and the number of transitions were reduced by a factor of 6. Thus, using this model in place of its more complicated orignal model for system-level performance analysis would yield a significant run-time improvement.... ..."

Cited by 1

### Table 4: Meaning of Places in Petri Net Place Meaning

"... In PAGE 48: ...RRR ??? 8.3 Using Petri Nets A Petri Net model of the uncontrolled plant is shown in Figure 22, and the meaning of the places is given in Table4 below. Notice that we have modeled the system such that machine 3 loads one part at a time.... ..."

### Table 1. Corresponding Petri net and graph transformation variants

2002

"... In PAGE 2: ... Based on the correspondence of Petri nets and (typed) graph transformation, which regards Petri nets as rewriting systems on multi-sets of vertices [5], we can derive a model of time within typed graph transformation systems with attributes. The corre- spondence is visualised in Table1 . Besides (low-level) place-transition nets and typed graph transformation systems, it relates (high-level) environment-relationship nets to typed graph transformation with attributes.... ..."

Cited by 3

### 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.... ..."

Cited by 22

### Table 1. Corresponding Petri net and graph transformation variants

"... In PAGE 2: ... Based on the correspondence of Petri nets and (typed) graph transformation, which regards Petri nets as rewriting systems on multi-sets of vertices [5], we can derive a model of time within typed graph transformation systems with attributes. The correspondence is visualised in Table1 . Besides (low- level) place-transition nets and typed graph transformation systems, it relates (high-level) environment- relationship nets to typed graph transformation with attributes.... ..."

### 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... ..."