"... In PAGE 5: ...robability of 0.5. The keys were chosen from a uniformly distributed random variable. Table4 shows the performance results for actual execution time and Petri net simulation... ..."

"... In PAGE 15: ...48 The work of Genrich et al.41 is an exception to the classification shown in Table3 . In their model, the color of the tokens is associated with the concentration of the molecular species in order to make a quantitative analysis.... ..."

"... In PAGE 10: ... In fact, these two types of state machines are two views of the same underlying executable state transition abstraction from two different perspectives. Actually that underlying executable state transition abstraction can be transformed to a global Petri-Net defined by the conversion rule in Table1 . That executable state transition abstraction provides a better and simpler representation than Petri-Net does but with same semantic.... ..."

"... 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.... ..."

"... 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.... ..."

"... 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... ..."

"... In PAGE 7: ... In order to logically synthesize a given STG, using Petrify, it is necessary to check that it is free from safeness and liveness problems. The statistics obtained after veri cation are listed in Table1 . This table presents the number of condi- tions and events generated from each of the models.... ..."