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ComputerAided_Design_Engineering_amp_Manufactur.pdf

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FIGURE 8.4(a) Generate a new IG using PP rule. (From Reference 2a. With permission.)<br />

1 2 3 4 5 6<br />

1 CN CN CN CN CN CN: Concurrent<br />

2 CN EX CL CL CL EX: Exclusive<br />

SE SE<br />

3 CN EX CL CL CL SE: Sequential<br />

SE SE Earlier<br />

4 CN CL CL EX CL SL: Sequential<br />

SL SL Later<br />

5 CN CL CL EX CL CL: Cyclic<br />

SL SL<br />

6 CN CL CL CL CL<br />

FIGURE 8.4(b) An ex<strong>amp</strong>le of the matrix to record the relationship between PSPs. (From Reference<br />

2a. With permission.)<br />

( �nps) DEP2 and vice versa. nps is called a prime start node. If nps � P, then �1|� 2. �1��2 if none<br />

of �1� �2 , �1 ↔ �2 , and �1 o �2 hold.<br />

Note �1��2 implies nps � T or �1 and �2 are in two separate components of a PN that is not<br />

strongly connected. Also, in any synthesized PN using the TT and PP rules, �1 cannot be both concurrent<br />

and exclusive to �2 using the above definition. This is, however, not true for PNs that cannot be<br />

synthesized using the TT and PP rules.<br />

The above definition of sequential, earlier, and later seem to be also marking related. However, in the<br />

synthesized net, any cycle contains at most a place marked with tokens; thus the marked place can be<br />

considered a structure. In Figure 8.3, the new PSP � is and . In Figure 8.4(a),<br />

and are on an elementary cycle containing and ; hence in this figure.<br />

The structural relationship between any two PSPs is recorded in a matrix. An entry corresponding<br />

to row i and column k represents the relationship between and . For ex<strong>amp</strong>le, if is concurrent<br />

w<br />

�1 �2�� w<br />

�1��4. �3 �6 �3, �5, �6 �3 o �6 Aik �i �k �i

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