### 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 3: Synthesis of Petri nets from speed-independent circuits.

1998

"... In PAGE 32: ...2 Bottom-up approach: analysis of concurrent systems PN synthesis can also be used for the analysis of systems. Table3 describes the results of the ap- plication of our algorithms to the synthesis of Petri nets from TSs obtained from speed-independent circuits (all examples are described in [32]). This can be used to produce a user-readable description of the functionality of a circuit, in the form of a timing diagram-like labeled Petri net (a Signal Transi- tion Graph, STG).... In PAGE 32: ... Another potential application is to optimize the input to direct synthesis methods, that have been devised for Petri nets using both synchronous and asynchronous circuit design tech- niques ([39, 8, 44]). Figure 16 illustrates one of the examples shown in Table3 (a4 tflo1). Initially, a TS is derived by calculating all reachable states of the circuit (symbolic techniques can be used here).... ..."

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### Table 4. Validation of Petri net model

2005

"... 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... ..."

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### Table 2: Synthesis of Petri nets from speed-independent circuits.

1995

"... In PAGE 21: ... The rest of the synthesis method for UC and FC nets remains the same. 7 Applications Table2 describes the results of the application of our algorithms to the synthesis of Petri nets from transition systems obtained from speed-independent circuits. This can be used to produce a user- readable description of the functionality of a circuit, in the form of a timing diagram-like labeled Petri net (a Signal Transition Graph, STG).... ..."

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### Table 2: Design patterns in Petri-nets

### Table 2: Synthesis of Petri nets from speed-independentcircuits.

"... In PAGE 6: ... More on that is also in [4]. 5 Applications Table2 describesthe results of the applicationof ouralgorithms to the synthesis of Petri nets from transition systems obtained from speed-independent circuits. This can be used to produce a user- readable description of the functionality of a circuit, in the form of a timing diagram-like labeled Petri net (a Signal Transition Graph, STG).... ..."

### Table 3: An execution sequence of the Petri Net in Figure 3. Since, places F and FF are coloured, the colours (order numbers) of their tokens are shown as well. Place H is also coloured and the colour of its token is N+1, if N occurrences of E have 21

1997

"... In PAGE 3: ... We can solve these problems by providing a much simpler set of Datalog1S rules, that still models precisely the execution semantics of our example Petri Net and also maintains the one- to-one correspondence between external basic events and stages. This is achieved by folding the sequence of stages (states) in Table3 into the one in Table 4. In the new table, each external basic event creates only one new stage.... ..."

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### Table 1: Petri net modeling elements Sign of Each Element Description

"... In PAGE 3: ... The basic structure of PN includes (i) a finite set of places ; (ii) a finite set of transitions ; (iii) a finite set of arcs ; and (iv) a set of tokens that define the initial markings. The signs commonly used for denoting the place , transition , arc and token are illustrated in Table1 . In essence, the arcs define the input and output functions which govern the flow of tokens from places to transitions and from transitions to places respectively.... ..."

### 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.... ..."

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